how does the "gift" option work in creating a give away

You must add the winner as a Steam's friend (and he should acept the request), and then sent the gift

You can send the "gift" directly in steam by adding the winner of your giveaway to your friend list.

Also, make sure the person receiving the gift is from the same region/country as you are if you are not using a key or gift link.

Regional/country pricing could restrict who you can send the gift to if you bought it from the steam store itself as their currencies may have different values.

Best to use a bundle site like Humble Bundle or Fanatical to get a key so you can add it in and send it right through this site.

As for the choices in SG -
Gift can be used like others mentioned when you want to add someone in your friends list and send them directly on steam store. OR when you want to send the key AFTER the giveaway ends. I personally choose not to reveal my keys on humble instantly when making GA as I don't want risking it sitting there for a week and something going wrong. I prefer to reveal the key only when the giveaway ends, I have seen the winner and then I send the key to him/her. That's when you can use gift option here, because that lets you create giveaway without adding the key instantly

But as others already pointed out -regional pricing is pain in the ass.. so you have to be careful setting region locks when creating giveaways if you plan on adding and sending an actual steam gift