Some teapots are made of porous materials like terracotta, sandstone or clay for instance. These teapots will absorbe some tea particles called tannins. They’ll keep a trace of every teas that has been brewed inside them. And thus will reveal deep tea flavors.
Progressively tannin will coat the inside of the teapot. However this process requires lot of patience and know-how to get good results.
It’s said that tea Masters’s teapots have great value.
This coating process implies that one should not infuse different types of tea in the same teapot. Best practice would be having a teapot for each tea family (green, yellow, dark, black, blue-green, white, and smoked). A teapot for a tea.
There are also many teapots made of other materials such as cast iron, metal, porcelain, glass and so on. They won’t absorb any tannin and therefore will not (or almost not) keep memory of passed teas.
A teapot should never be cleaned with soap or any other product. Just rinse it with hot water. For thorough cleaning just use a little coarse salt and that should do the trick.
Do not shut between uses to prevent mold.