Decaf black tea is black tea that has undergone a decaffeination process to remove most of the caffeine that occurs naturally in tea leaves. The result is a very similar product that won't keep you up at night!
When tea is "decaffeinated" it means the tea has gone through a process to remove the majority of the caffeine. Decaf teas still contain some caffeine, but in much smaller amounts than their caffeinated counterparts.
Caffeine is naturally occurring in tea and therefore must be removed to create decaf tea. Any real tea (made from the camellia sinensis plant - including black, green, white, and oolong) contains caffeine. "Caffeine-free" means the caffeine was never there in the first place, as in herbal teas.
For a product to be labeled "decaffeinated," the amount of caffeine cannot be greater than 2.5% of the original caffeine content, according to U.S. regulations. The residual caffeine left over after decaffeination is approximately 2 to 3 mg per cup of black tea. Black tea that is not decaffeinated contains 15-70 mg of caffeine per cup.
No decaffeination method removes the caffeine completely. Find more information on caffeine in tea.
Looking to reduce your caffeine consumption? You can lower your caffeine intake without giving up black tea! Here are some tips:
Some websites and other sources will tell you that tea can be decaffeinated at home by steeping the leaves for 30 or 45 seconds and pouring off the water. This method has been disproven.
While it's true that caffeine is water-soluble, it takes much longer than 30 or 45 seconds to remove the caffeine. If you steep your tea long enough or enough times to remove a significant amount of caffeine, you would be left with some extremely watered-down tea.
See Dr. Weill's answer to the at-home decaffeination question.