The Oxford Dictionary describes a 'symbol' as a: '1. thing regarded as typifying or representing something . 2. mark, sign, etc. representing an object, idea, function or process; logo.' And I guess that's a start...
I'd say that the notions of 'carrier of meaning' and 'referring,' or 'representing' are crucial elements in the definition.
So a symbol could be described as a thing that carries a meaning that refers to, or represents, the meaning of another thing.
David Fontana uses 5 categories of symbols, which is quite useful. He distinguishes:
Lots of symbols have been added to the exopaedia; currently there are over 370 definitions. Use the search facility, or the 'related topic' to find them.