An idiot straight is the worst straight possible on a 4-to-a-straight board. Anyone can see that a straight is likely, and it is unlikely that a player holding the idiot straight is going to get much value from his hand. But idiots will still bet here, and call a raise - hence the name.
Example: On a board of 289TJ, villain bets the river with 74, the idiot straight. Hero calls with Q9, scared of the flush and because he has butchered the hand already.