The Clan Karma system is a way to prevent clan looting, determining how much you can take daily from the clan stash. Every item has a karma value equal to its autosell price. Adding something to the stash adds its karma value to your karma, while taking something out costs you that amount of karma.
The amount of your karma you can spend per day can be set by the leader of your clan. They can give every rank a karma limit from 0 to 10000, or set no limit at all. Most clans have a ranking system where each new rank gives you a higher limit. To get to higher ranks, and thus be able to take more from the clan stash, you usually need to be active and donate things to the stash.
You can also gain karma by donating meat. The meat:karma ratio in a clan is determined by the clan's administration.
Tradeable items without an autosell price that can be added to the stash can only be withdrawn by ranks that have been specially enabled. There may be a daily limit on withdrawing zero karma items. The most common zero karma items are Mr. Accessories, stuff purchased from Mr. Store, and some other (usually valuable) rares. See also Items by autosell price (0 Meat).
Many people claim that the karma system is unable to stop the looting of clans, as many items have a karma value much lower than their market value (eg, a sword behind inappropriate prepositions, which can be obtained in the Clan Stash for 135 Clan Karma but are often available in the mall for 40 thousand meat or more). Jick has stated that the clan karma system may not work perfectly, but that it should be usually sufficient to combat the problem of clan looting as long as you only let people into your clan that you trust, and that you give reasonably low karma limits as a leader.