Jabbering usually implies speaking very fast, often too fast for others to follow. He began to jabber as soon as he got nervous.
Pro Tip 2/3
Informal Context
Used mostly in casual conversations, 'jabber' is not typical for formal situations. At the party, they would jabber excitedly with their friends.
Pro Tip 3/3
Lack of Clarity
'Jabber' also suggests that what is being said is hard to understand because of how quickly it's spoken. Amidst his jabber, I could hardly catch a word.