Of the many things that one can do, this is possibly one of the most versatile in terms of reason and purpose. The act of being alone can occur in many different ways and take many different forms. You can be alone in a crowded room, or simply alone in your head.
A common image of alone is that of a person without whom they can share themselves; the lack of a significant other. This is definitely a valid view (and one that I can relate to). In this instance, being alone may or may not be a negative thing. Many times, this state is one not chosen actively, but one simply of bad fortune and/or situation. Other times, it may be a purposeful decision, which I will talk about shortly.
"Being alone" does not imply loneliness. While that case may be true some of the time, it is by far not the only definition. To be alone is often times an actively chosen state, not a passive occurrence. There are many reasons an individual would choose to be alone. One may choose to be alone to assemble their thoughts, take something into consideration, or just simply have time to themselves. They may also desire to be alone because they are hurt, depressed, or overwhelmed -- as the case may be when one has been dumped or is over-worked.
Introverts also fall into this idea, as they thrive on having time to themselves; they find such an activity rejuvenating and reinvigorating. A need to be alone for an introvert is especially important after being with a large group for a period of time; interaction and sensory overload lead the introvert to the need to be by themselves.
In many circumstances, being by one's self can often be a combination of these things. It can be fantastic, or it can be absolutely awful (or somewhere in between). In the end, though, no one is alone forever and that is something everyone can rely on.