it implies leaving/moving.
it's true that there are small bags that are used to hold things.. but generally when people say 'I'm gonna pack up my ditty bag" they're not being literal - it's slang for leaving.
MacGyver: It's the ignition. I'll use the batteries from the flashlight in my Ditty Bag to start it.
Joe: Oh no, my luggage won't stay together.
MacGyver: Use one of the zip ties in my Ditty Bag to hold it together.
Joe: Oh no, I have a head ache.
MacGyver: I'll give you some of the asprin from my Ditty Bag.
Joe: Oh no, my space suit is leaking.
MacGyver: I'll plug the whole with some of the silly puddy from my Ditty Bag.