Steam trading cards are typically used to level up your Steam profile and the badge to that game.
Steam Badges have 5 levels, each level granting 100xp to a maximum of 500xp at the level 5 badge. The xp granted after crafting a badge goes towards leveling your Steam profile, and you must have a full set of cards for that game to do so.

Important to note: Each time you level up the badge it will change appearance, so you may want to check what it looks like at each level!

A great website that shows all the information you need to know about a games' trading cards, badges, emoticons, and backgrounds is Steam Card Exchange[www.steamcardexchange.net]

Each game has two types of badges, the normal badge which was discussed right above^ and a foil badge. A foil badge can only be crafted once for 100xp, and is typically more rare, expensive, and needs foil trading cards to be crafted.

Here is the complete levels and badges for Assassin's Creed Odyssey:
Foil Badge:



(Screenshots taken from Steam Card Exchange: Assassin's Creed Odyssey[www.steamcardexchange.net])

Upon each time you craft a badge of any sort you will also get a Steam emoticon and background. Here are both of those for Assassin's Creed Odyssey. (They can also be bought through the Steam market like Steam Trading cards.)
Emoticons:


Backgrounds:
Athens
Sparta
Statues
Trireme
Alexios
Kassandra

Thank you for taking the time to check out my first Assassin's Creed Odyssey guide! I know it's nothing special like some of the more in-depth guides, but I hope this guide does help someone! If you have any questions or need help feel free to ask! - Brian.