When you convey something, you carry or deliver it. Little Red Riding Hood conveyed a basket of muffins to her grandmother. Your sad smile might convey more about your feelings than words ever could.
You can also convey a message or information, which means that you communicate it to someone directly or indirectly through your words or actions. In law, the word convey means to transfer or pass property to someone. This verb is from Middle English conveyen, from Old French conveier, ultimately from the Latin prefix com-, "together," plus via, "way."