i hear your words, i call my name

To belong to a Generation - what does that mean?

What does that actually mean. The dicitonary defines "Generation" as

a. A group of individuals born and living about the same time.

b. A group of generally contemporaneous individuals regarded as having common cultural or social characteristics and attitudes: "They're the television generation" (Roger Enrico).

One associates to belong as a form of security, a form of posession. Does belonging to a generation mean a sense of security? but what of those who feel they were born at the wrong time and in the wrong generation? What then?