A Dallas straddle, much like any other straddle, is a bet that someone can make preflop before cards have been dealt. It's typically two times the size of the big blind, but some venues allow players to Dallas straddle for any amount that they wish. Only the player on the button can make a Dallas straddle.
What's unique about this type of straddle is that the straddler gets “absolute last action” preflop. This means that as long as there's a bet or raise and any other player remains who has not folded, called, or re-raised, the action skips over the straddler. He or she only acts after everyone else has completed their decisions.
For example, let's say the button makes a Dallas straddle to $8 in a $2/$4 NL game. The action starts at UTG – to the left of the big blind like normal – and it folds around to the cutoff who makes it $20 to go. The person on the dealer button would normally act next, but in this case, because they straddled, the turn of play bypasses them and goes to the small blind instead.
Let us suppose that the small blind calls the $18 back to him, and then the big blind re-raises to $60. Now the cutoff folds. Instead of being the dealer's play, the action skips him yet again, and the small blind must decide whether or not to put the additional $40 into the pot, fold, or four-bet.
If the small blind either folds or calls, then the dealer position gets to make his moves. If the small blind four-bets, then the action is on the big blind, and if the bb player re-raises again, then the small blind will have decide first before the player on the button.