Welcome.  The node is what's called a "full node", it downloads the entire blockchain and verifies all transactions and blocks.  It's needed if you plan to solo mine.  It's also a command line wallet, you can check balances and make transactions, but it doesn't have a nice GUI to do those things for you. 

The web wallet on the other hand doesn't require downloading the full blockchain, and has a more user friendly interface for sending/receiving aura and deploying smart contracts.