Relationships are the first thing that come to my mind when considering Type Two. It's one of three Enneatypes (2, 6 and 9) that are called the "relationship-oriented" types, because these types tend to care a lot about others and understand more readily than any other Enneagram type that the greatest sweetness and most important thing in life lies in serving others with selfless dedication.
Since Type Two is located in the Image Center (comprised of Types 2, 3 and 4), however, there is a key difference between Type Two vs. Types Six and Nine. Image Center types (when entrenched in, rather than liberated from, their programming) are all deeply self-conscious and fixated on ego issues/how they are viewed by others. Have you heard the statement that "humility is not seeing yourself as more than you are, nor as less than you are, but just as you are"? That's a very profound statement, because indeed, characterizing yourself as inordinately low, wretched or worthless is just the flip side of the coin from seeing yourself as special, above-average, and better than most others; and Image Center types are the ones who have issues with this sort of thing. Types Six and Nine have no issues in this department, so for people with those core types, questions about their self-worth don't normally arise. Although growing up with abuse and shame or excessive praise and attention will certainly affect core Sixes and Nines too (since we all do have an image fix somewhere in our programming), their natural tendency is toward the humility of self-acceptance; neither making too much of themselves, nor excoriating themselves endlessly for making a mistake. Their biggest issues are in other areas. But Image Center types mask a deep-seated sense of shame and worthlessness with various types of pride. Type Fours pride themselves on being different, original, creative, unique and authentic individuals; competitive Type Threes on simply being the best at whatever they do; and Type Twos on their selflessness and loving, caring, other-oriented nature. Thus, the selflessness of Type Twos, whether they realize it or not (they usually don't until it's pointed out to them), is self-conscious and at least a little bit vainglorious. Ordinarily, Twos tend to have a very good image of themselves. Their natural inclination is to think of themselves as wonderful and great (though usually not to the degree that would make them odious or annoying to others!) because they're so nice to and do so much for everybody. But their hope and expectation is that others will take notice of this and respond with lots of love and appreciation for them, and will reciprocate with their serving and giving by doing loving things for them in return. If they are dissatisfied with the amount of appreciation and reciprocation they're getting from others, they may try to tolerate and push on with their program of selfless service for some time, but eventually, Type Two will "go to Eight," which means explode and start yelling and chastising others for not doing their part. And on the other hand if it's the Two who makes a mistake, they'll tend to beat themselves up about it rather excessively, because they have a deeply ingrained belief that they aren't enough just in themselves, but have to earn the love of others through good behavior. The direction of growth for Type Twos involves "going to Four" -- i.e., learning to be in touch with themselves and their own needs and learning to express those openly and honestly as and when they are felt, rather than suppressing them and trying to maintain an artificial facade of total selflessness in order to earn the love of others, which leads to frustration (and possible self-worth crises) when the Type Two is not satisfied.
Another basic characteristic of Twos is that they belong to the positive-outlook triad (2, 7 and 9), so they tend to look on the bright side, hope for the best, praise and encourage good qualities in others, be very cheery, etc. (Twos dearly love to give and receive compliments. They themselves are very sensitive to how they're viewed by others -- criticism and rejection hurt them badly. Whether they've had the opportunity to realize it or not, they're somewhat dependent on external validation to maintain their good self-image, and since they're caring, they want to share that which they need and enjoy with others.)
Also, as mentioned in my last post, Two is in the compliant triad (Types 1, 2 and 6), which means it's one of the Enneatypes that have a Superego inside their heads telling them constantly what they ought to do, and they feel obliged to comply whether they feel like it or not, and whether they have energy or not. These types generally try to be very responsible, dutiful and diligent, cooperate with the needs and requests of others as far as they possibly can, and feel bad if unable to fulfill others' expectations. They're fully involved participators in life and relationships -- not checked-out, uncooperative, stubborn or lazy like the withdrawn types (4, 5 and 9) can be perceived as being at times -- but they don't have as much driven, dynamic, fiery, raw energy as the aggressive types (3, 7 and 8). Compliant types' efforts can be plodding (though they have more energy than slow, easygoing Type 9 usually exhibits), but whatever is on their list, they'll keep at it dutifully until it's done. (With a generous 3-wing, by the way, Type Two can be highly energetic, active and goal-oriented, so keep in mind I'm not saying their efforts WILL be "plodding," just that they can be.)
The combination of caring about people plus having the sense that they know what needs to be done produces in Type Two the frequent tendency to give others well-meaning advice and/or to try and organize people to get the job at hand done. Indeed, Twos are part of a triad (2, 5 and 8) whose types all have a certain level of desire for power and control, which in Two and Five can even be hidden from themselves. In Type Two this usually manifests in a sort of "power behind the throne" mentality -- the desire to encourage, enable, and advise others (and of course take part themselves in whatever way may be necessary) so that the needful can be achieved. When frustrated or unhealthy, they may become annoyingly bossy (some Twos tend to assume the role of "parent" toward others, who may not welcome being parented), but when happy and healthy, Twos are usually very sweet and kind in the way they express themselves, and try their best to be sensitive and careful not to get on anyone's bad side. Twos generally never want to let go of any relationships; they usually try to hang onto and keep in touch with all their family and friends forever, so they have to be more careful than, for example, free-wheeling and unattached Type Seven, not to offend anyone.
The natural parenting ability of Twos finds its best expression, of course, in dealings with children, whom Twos tend to adore. I've never met a Two who didn't love kids, and kids love them in return. Twos' love of babies and adoration of motherhood may play a part in a phenomenon I seem to have noticed, although I've never read about it anywhere -- namely: I'm under the impression that Type Twos often have passionate love and appreciation for and deep interest in pregnancy and the process of birth.
One last tidbit is that Type Twos are said to often have the habit of feeding their emotional needs with sweets and carbohydrates, especially when they feel like they're not getting satisfaction in other ways.
Now then -- the wing types:
Type Two can of course have a prominent 1-wing and/or 3-wing. When the 1-wing is prominent, the Type Two person will tend to be less energetic and more dutiful, since One and Two are both compliant types. They'll be more concerned with what is ideal, moral, proper and righteous. Dedicated to their loved ones, and perhaps to a cause they believe in, they'll give of themselves by doing the needful endlessly with somewhat less expectation of recognition (since One isn't in the attention-hungry Image Center like Two and Three are, the 1-winger may be happy to work behind the scenes and not come out into the spotlight at all). 3-wingers, on the other hand, have more energy and sparkle. Often they love to organize and take part in creative performances, and they adore being cheered and congratulated. Due to Type Three's ambition and goal-orientation, a 3-winger may be overflowing with ideas about what he or she would like to accomplish in life. Since both Two and Three tend to be extroverted more often than not, a Two with a 3-wing usually loves socializing and entertaining people in his or her home, although an introverted 2w3 is not at all unheard of (my own mother is one -- though of course, not deeply introverted!).
Twos are capable of being some of the sweetest, most lovable and adorable people in the entire world if they can just be in touch with and expressive of their own needs, rest assured that they're worthy in themselves no matter what, and give others the space to reciprocate and cooperate with them or not, as those others see fit.