This is what the Holiday Insights Web site has to say:
What's all the chatter about over this special day? Well, on Babbling Day, we celebrate those of us with a glib tongue. You know them when you hear them. They're talking gibberish. They never stop talking. They babble on and on. They can turn a simple one sentence statement into an endless dissertation.
Spend this day babbling like a baby, if you must. As for me, I will spend it by a babbling brook.