You feel nostalgic when you miss your childhood, people you know but haven't seen in a while or the things that bring you comfort, like the nostalgic memories you feel when you listen to the songs you loved when you were little.
The adjective nostalgic is often used to describe someone who is homesick and wants to be back at home with family. It always involves a wistful memory of times that now seem better or simpler. A nostalgic feeling can involve home and family, but it can also involve a longing for long-gone moments. Even beloved things, such as old TV shows or athletes from a different era may provoke the feeling of nostalgia.