As Felipe says, "llevar" has more than one meaning. If you're getting confused as to when you should use llevar and traer (with the meaning of bring), it's pretty simple. If you or someone else is brining something to or towards where you physically are at the time of saying it, then use traer. If they are going to bring you something to another location, where you aren't physically at the moment, then use llevar.
Some examples might help.
TRAER
Bring me a spoon. - Traeme una cuchara.
Bring me a glass of water. - Traeme un vaso de agua.
Bring me anything to where I am physically right now.
LLEVAR
Bring it to work tomorrow (but I'm at home right now) - Llévala mañana al trabajo.
We're almost there, can you bring me a jacket? - Estamos por llegar, me llevas una chamarra?
Hope that helps.
