Eth is the native token, WETH is an ERC20 token (token creted by a contract implementing the ERC20 interface). Many applications don't want to handle these separately, so they only accept ERC20 tokens. WETH is Eth wrapped in a token contract (can be warpped or unwrapped 1:1). Think of it as similar to Java's int vs Integer.
Lots of different things live on the Ethereum blockchain: there's ETH itself, which we might call "raw money", and then there are abstract tokens (of both the fungible and non-fungible sort).
To make a programming analogy, there are lots of systems which are "generic" over tokens — they can deal with many kinds of token, as long as it's the standard shape. Raw money doesn't have this shape, so WETH is a very simple "wrapper token". You can trade 1 ETH for 1 WETH and then use it in some token-compatible system.
The exchange rate for WETH is fixed by the (very short) contract, and it's supposed to be simple to trade money for tokens or vice versa — although given this poor sod's story, it's arguably not that simple after all.
