Humans are social animals, and many of us find it comforting to know that other people are nearby, even if we are not directly interacting with them at the time, just as we find it comforting to know that there is food available even in moments when we are not experiencing pangs of hunger.
Once we might have build a house in a village, and sat on our front porch, watching the passers-by and exchanging brief greetings with them. Now, we build our profile in an electronic village, and sit at our computers, watching the passing icons and exchanging brief greetings with them. Occasionally, we may hear important news from these passers-by, or invite one in for tea to sit awhile. Most of the time, we will instead soothe our psyche by reaffirming their presence and quiet our hindbrain by showing it pictures of its tribe.
We are all suspicious of people who appear out of nowhere offering a deal or opportunity; they are likely to have deceitful and self-serving intentions. Similarly, others will have the same suspicions of us; if we wish to approach someone with a request or invitation, we may find it helpful to be introduced by a mutual friend.
Online social networks serve as a convenient repository for these introductions. We can see that someone we may not know well has five mutual friends; this bypasses the initial mistrust and serves as an introduction. Similarly, if we meet someone at an event and wish to keep the acquaintanceship active in case we have business at a future time, we might once have taken this person's business card, put his or her address on a list, and sent Christmas or birthday cards to keep ourselves in their memory. Adding the person on a social network is a faster and less expensive alternative.
Thus, the benefit of the extended online social network is not that it provides meaningful interaction - it is that it provides, at low cost, the option of initiating a more meaningful interaction at a future time, bypassing the expensive and difficult initial step of introduction and suspicion alleviation.