Function signatures in the Ethereum Virtual Machine (EVM) are specified by the first 4 bytes of the data sent within a transaction. The "Ethereum Signature Database" is a collection of function- and event signatures which makes it possible to recover the function- or event name based on its hex signature.
Using the database you can get a better understanding as to what a transaction did if you only have access to the transaction data and not the source code of the Smart Contract in question.
- Snake Charmers