A good example of a real, everyday use case for smart contracts is NBA Top Shot. Unlike regular collectable the smart contact guarantees the company cannot decide to manufacture more of a rare item, it allows verification of the supply and traded value.
A lending contract like Aave simply formalises the economic contracts behind lending. By doing so it can provide stricter guarantees about enforcement. It's not so much of a contract but a strict set of bindings that the EVM will enforce.
If you've stayed away from binance perhaps you've used or hear of atomic swaps? They're especially smart contacts that aren't tied to any chain. A strict set of rules and moves to guarentee that the contract of swapping is withheld by both parties.