Feeling of belonging is a very important concept. Consider being in a relationship, where you feel like an alien most of the time or working a job which makes you feel all the time that it is just not what you want to do or, living in a place where you feel you are a stranger and are hardly able to relate yourself with anyone or anything there. These were a few examples of what I feel are the feeling of 'not belonging'. Some associated concepts are cultural shock, which is essentially a feeling of not belonging to a certain culture and place; identity crisis which is essentially a feeling of not belonging anywhere in life among peers, among elders etc etc.
It is convenient to say that all this lies in our mind. If you were a proponent of humanistic psychology, you would notice Maslow's theory of Needs (Please use google to study the theory :P), which specifies as one of the needs - the feeling of belonging and acceptance, love etc. Feeling of belonging is a very fundamental need at various stages of life and not just during childhood and young adulthood. In my opinion there is a paradox here. At first you don't have a feeling of belonging and you tend to be on the quest for somewhere to belong and try to reach out to sources which offered you sense of belonging atleast during childhood. On the contrary, there are people who just adapt themselves to situations and bring in a sense of belonging for themselves, which can probably be summed up as being a Roman in Rome. As we have evolved as humans, we have adapted ourselves to the environment and learnt to improve our lives. Even though it is hard to say how the need for belonging was fulfilled, in my opinion the need for belonging was superimposed by a more important need which was of mere survival.
For me a sense of belonging is extremely important. The point I am trying to make here is that at any point, implicitly or explicitly a feeling of belonging is inevitable. If you are trying to connect with people on very professional level, sometimes you do that only for the sake of getting your work done or for so-called networking. But even then, your comfort level with people increases when there is a mutual effort to make conversations slightly on a personal level of course within certain bounds. As an example, in my opinion when you address people with their names more often during conversations, it makes the other person more comfortable. Similarly on a personal level, when a person individually tries to adapt to the society, the culture, the place he lives in, the people around him, a sense of belonging becomes a supreme need, the lack of which affects the day to day life of the person.
Overall, summing the whole thing up, there is a quest in people to find out where they belong, until which nothing really makes them feel satisfied in life. As for me, I am still searching where I really belong and hoping that there is somewhere I do belong and that I would find it soon.