A change bag is a cloth bag with the edges of its opening sewed to a wooden hoop on the end of a stick. Originally, many centuries ago, magicians use such a bag to collect donations from onlookers, and the bag got its name from the fact that donations were generally in the form of small change. Magicians often carried their money in the change bag between shows, making them the target of robbers who found the bag-on-a-stick a tempting target, hence the term "stick up."
Because they were always getting robbed, magicians decided to find a way to make their money "disappear" when danger threatened. To this end, they created a bag which could be filled if held one way, but if the handle is turned 180 degrees (turning the bag face down) and the bag is gathered and pushed through its wooden frame, effectively turning it inside out, it will become completely empty. If you construct a change bag of your own (all you need is a needlepoint hoop, a cloth bag, a wooden spoon, needle, thread, glue, and a battery-powered point-location phase-distortion vanisher), you'll see how easy it is to use.
Note: A "change bag" is an entirely different thing from a "coin purse" -- don't be fooled!