No matter if you download or purchase a sound effect, it comes with a license attached to it. This license is a legal agreement between you and the owner of the sound. Like most legal agreements these days, you do not have to actually sign a copy to enter into the agreement, the download or purchase is considered as your signature. It is important to understand that not all licenses are the same, but the core point is usually similar.
That sound effect you just downloaded/purchased does not actually belong to you, you do not own it. You are simply purchasing the right to use the sound effect in a work, be that a film, radio commercial, cell phone application, video game, etc. This means that you can not sell or give the effect to anyone else. You are however permitted to sell and distribute the work that you have used the sound effect in. You can also use the same sound effect in many different works without having to pay the copyright owner any more money.
A term that you should become familiar with is Synchronization. In the world of sound effects, this term is a way to explain how you can use the purchased or downloaded audio in the works that you create. Essentially you are taking the sound effect, and syncing it to a visual creation, or other audio creations, it is not the main focus of the work. If you were to try to use a sound effect as a beeping sound of a toy, this would not be synchronization, and would not be permitted.
It would be wise to always check out the specific end user license agreement (EULA) when you are looking to download or purchase a sound effect. Never assume that you are going to be able to use the sound effect the way you want to until you confirm it. If you are still unsure after reading the EULA, get in touch with the owners to put any doubts to rest. It is better to ask and be sure, then to suddenly find yourself in trouble regarding the use of the sound effect!