You can request common and rare cards in your clan, and it is obvious that this is beneficial for the receiver (you get free card(s)). What is in it for the donator?
To add to the above and expand, and probably what is the best reason to donate is: You can get up to 4200 gold per week from donations. Explained here! If you are in a big clan (40-50/50) you will be able to always donate cards reach your daily limit, and yet keep the cards that are currently valuable to you.
For instance: as I constantly save up and don't level the common crap in my deck I have 15 different cards that I can level up, most of them more than once, AND I also have 5k gold on 1300 trophies. Most of that is from donation in my clan, where last week I had donated ~240 cards. I don't donate the one common and one rare I have in my deck, and donate everything else. I initially checked whether or not a player donated to the clan, but we recently had a good clean and all players are decent now.
If you donate a common card (up to two per request) you get 1 experience and 5 gold.
For a rare card donation, you'll get 10 experience and 50 gold.
Apart from that, many clans have a 'donate-or-leave'-policy. In the clan the number of weekly donations is visible, and no-donators can be kicked out, if your clan is that strict. Furthermore, the feel-good factor in a clan goes up when there are a lot of donations, possibly increasing the chance that your own requests will be granted.
The Donation limit has now increased in Higher Arenas, like the Royal Arena and the Frozen Peak, you can Donate up to 200 Commons per day! (Or their Rare equivalent) This means that you can get up to 1000 Gold / 200 XP from Donations daily!