Translation:These are vouchers for the restaurant.
Is 'Gutscheine' something like a coupon (a deal that gives you a discounted/free item on purchase), or would it be more like a gift card (an item that allows you to get items at a store without having to spend money)? We do not use the word 'voucher' much where I'm from and I'm having a hard time understanding how this word translates
It's talking about a discount type coupon/voucher (eg. 1000 extra nectar points when you spend £5 on bread/Free dessert with every main/whatever). I'm not sure where you're from but here voucher and coupon are used pretty interchangeably.
Gift voucher would be Geschenkgutschein.
I'm very curious. where are you from where people don't say voucher?
Since most of the discussion seems centered on the difference (if any) between voucher and coupon, let me offer my two cents. When you vouch for someone, you are telling a third party that the person is good for some purpose/thing. Following that thought, a voucher in a monetary transaction represents that the entity issuing the voucher will pay (make good) the vendor for the goods/services given to the voucher bearer. The goods/services may or may not be discounted. It is completely possible that the vendor will receive full (not discounted) value. A coupon, on the other hand is a two-party transaction (the voucher is a three-party transaction: the buyer, the seller and the payer). A coupon is an offer by the seller to sell at discount, or with some other incentive of value, stated goods/services to the coupon bearer. More often than not, the buyer will have to pay something with a coupon. With a voucher, the buyer pays nothing so long as the limits on the goods/services stated in/on the voucher are not exceeded.
In English, you could say 'to a restaurant' however, the sentence here in german is "Das sind Gutscheine für das Restaurant." It has the word für, therefore it wants you to translate it with the word 'for' and also 'to a restaurant' wouldn't work as the sentence says 'das Restaurant' so you would have to say 'to the restaurant', but 'for the restaurant' works best here.
Generally, the hints will give you the correct words for the sentence (if not you can report it) however, you still have to use the words in an order that is grammatically correct in German. I'd suggest trying not to use the hints if you can help it, so you really learn to remember each of the words, I've found that that helps a lot.