A backdoor draw or runner-runner draw is one that needs two instead of one card to complete. If a player has three clubs, for example, then he has a backdoor flush draw in clubs. He needs two more clubs for the flush.
Example (Texas Hold'em):
The player has a backdoor flush draw in clubs and a backdoor straight draw. If the turn is a club, then he will have a regular flush draw. If it is a 4,6, or 9, he will have a straight draw.
Backdoor draws are not very strong, but can be helpful in close situations. The chances of getting a flush with three cards of one suit are around 4.2 percent. In the example above, the player has around an 8.5% chance of getting a six and therefore, and open ended straight draw on the turn, and a 17% chance of obtaining an inside straight draw with a 4 or 9 that could be completed with a 6. All in all, he has a 3% chance of hitting a straight by the river.