In finance, a long position in a financial instrument, means the holder of the position owns a positive amount of the instrument. It is contrasted with going short.
In terms of a security, such as a 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.
An options investor goes long by buying call options or put options on it.
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. If the price rises to above the strike price, the owner of a call option will probably buy the instrument and (at least on paper) will gain if the difference between the price at that time and the strike price is greater than the premium which he paid. With a put option on the other hand, the owner of the option will profit (on paper) if the price of the instrument goes up more than what he paid as premium even if he doesn't exercise the option. If the price ends up below the strike price he will be better off exercising the option to sell at the strike price, but whether he gains or loses depends on how much the instrument was worth when he bought the option. If the price drops below the strike price and he still has the instrument at the maturity of the option, then he's better off having the option (and using it) than if he didn't have the option, but of course he had to pay the premium in order to have the option.