It means having you identification checked to see how old you are. It happens when you buy alcohol or try to enter a bar that sells alcohol. Some states in the U.S. have stricter laws about carding than others. In some states, they only card a person if they look very young. In others, like my home state, you can look 100 years old and they'll still card you.

carded can also mean penalized, like in some sports games, i.e a red or black card

Wow this must be an American-ism! I had no idea what it was! For additional information, in the UK, we call this "getting IDed" (ID for IDentification made into a past tense verb!) I believe both must be very informal and colloquial!