When someone starts to jabber, they start talking on and on about this or that, or that or this, in an excited, sometimes incoherent way. Jabber is a close cousin to blabber.
When someone jabbers, sometimes their words seem to fly out of their mouths like quick punches (jabs!) from a boxer. Some examples of jabber? You know, like when someone has a hobby that you don’t really care about or understand but they won’t quit talking about it? Yeah, they jabber. Or your best friend is relating, without end, his excitement about the coming tiddlywinks championship and you comprehend neither the game nor its importance? That friend jabbers, too.