The action of telling the begining and/or middle of the story without revealing the the most interesting point (which usually occurs towards the end). This is most common when telling secrets, sexual stories, gossip, or embarassing situations.
The act of giving the "Dry Stick" usually occurs when the person is telling the story then realizing how embarassing, ridiculous or stupid the story or tale is. Then set person regrets starting the story-telling and therefore gives you the "Dry Stick" by not revealing the last section.
To see how to redeem a "Dry Stick" see Wet Stick
"So we were sitting in the car and my finger somehow ended up in her..no no wait I can't say it."
"Come on.. don't give me the dry stick."