A tea strainer is a device placed over a cup and catches tea leaves as the tea is poured through it. It is equipped with a fine mesh to filter out the leaves.
When tea is brewed the traditional way in the teapot, the leaves are not packed in teabags. It means they are freely floating in the liquid. As the leaves themselves may be distasteful, and their staying in the liquid during the time longer then necessary for brewing can make tea stronger and more bitter, it is usual to get them out by filtering through a tea strainer.
Strainers usually fit on the top of the cup and hold the leaves as the tea is poured through them, when you brew in a pot.
This is a double-layer fine mesh strainer, working better than regular ones.