A straddle essentially is a play on volatility. Ultimately, a straddle allows the owner to profit based on how much the underlying moves, regardless of the direction of the move. You pick a point around which to base the straddle.
Long Straddle: Long call A, Long put A
Put on a Long Straddle if the market is near A and you expect it to start moving, but are not sure which way it will go. Profit is open-ended in either direction, and loss is limited to the cost of the spread.
Short Straddle: Short call A, Short put A
Put on a Short Straddle if the market is near A and you expect it to stagnate through expiration. Because you are short, you reap profits as they decay, as long as market remains near A. Maximum profit is realized if market expires at A, but loss is open-ended in either direction.