teracota pots

It's algae. It happens because teracotta soaks up water and is often wet for long periods of time.

I don't think there is a permanent solution but putting the pot somewhere where it doesn't sit in water will help.

As Rydeboyz says, it is a green algae. You cannot stop it forming, I wish you could, but you can slow it down. After cleaning and drying the pots take a plastic kitchen pot scrubber ( the green scritchel pads) and put a very small amount of cooking oil on it. Rub this hard into the pot then use a clean cloth to rub off any excess oil.
A lot of my clays are in a sand plunge and only the rim of these goes green.