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Definition of Long Put: An investor is said to be long a put option when he has purchased a put option and currently owns the put. The term going long refers to buying a security, and applies to being long a stock, long a call, and long a put.
For those not familiar with the long straddle option strategy, it is a neutral strategy in options trading that involves the simultaneously buying of a put and a call on the same underlying, strike and expiration. The trade has a limited risk (which is the debit paid for the trade) and unlimited profit potential. If you buy different strikes, the trade is called a strangle. How straddles make or lose money. A long straddle option strategy is vega positive, gamma positive and theta negative trade.