In terms of a security, such as a stock or a bond, or equivalently to be long in a security, means the holder of the position owns the security and will profit if the price of the security goes up. Going long a security is the more conventional practice of investing.
Going long in a future means the holder of the position is obliged to buy the underlying instrument at the contract price at expiry. The holder of the position will profit if the price of the underlying instrument goes up, as the price at the contract was lower.
Different from going long in securities or futures contract, a long position in an option does not necessarily mean that the holder will profit if the price of the underlying instrument goes up. Going long in an option gives the right (but not obligation) for the holder to exercise it.
- Harrington, Shannon D. and Tim Catts, Sep 13, 2010, "Bond Buyers Getting Burned by Going Long as Yields Climb: Credit Markets", Bloomberg News