The pure (if you like) smart contacts do transactions. You give me 100 apple tokens and I give you 50 pear tokens. The contract ensures nothing else can happen.

They get more sophisticated e.g. automatic market makers. But same idea just swapping.

Voting is also possible e.g. release funds if there is a quorom. Who to release them to could be hard coded or part of the vote.

For external info from the real world e.g. "who got elected" you need an oracle. I.e. you trust someone not to lie and not to get hacked. You can fix the "someone" to a specific address but you still need to trust them.

That's a great explanation. I'm sure it's a lot deeper than that but I've never really understood the purpose. I'm not a crypto guy at all so it's nice hearing real world applications rather than just "stock market babble".