To Harrison someone is to give them something with very little left in it with the intent that they will finish it and then have to dispose of the wrapper/packet/container.
An example of this would be if you had a packet of crisps and asked your friend if he wanted them as you had had enough. Your friend accepts not realising there are only 3 or so left in the bottom, he has now been Harrisoned. Once he has finished them he must dispose of the packet in an appropriate manner.
"I just got Harrisoned didn't I?"
"It's really easy to Harrison Rob, he's so greedy."
"Luke is really good at Harrisoning people, isn't he?"