A symbol is a member of an alphabet. Sometimes a bunch of symbols get together in a specific order -- this is called a string. They have also known to appear on the tapes of Turing machines and similar devices.
Symbols are generally taken to be atomic, unless explicitly described as "compound". They are also generally considered to have a visual representation (or even to be that visual representation in the sense that they are specifically that, and not the thing that is being symbolized).
For example, the symbols of a binary alphabet in common use are 0 and 1.