Tea strainers are small strainers used in the serving of tea made from loose dried tea leaves. They are either designed to sit over the top of a tea cup, or be held there.
A pot of tea is made with loose leaf tea, then when it has steeped sufficiently, some tea from it is poured through a tea strainer into a cup. The strainer catches any tea leaves that pour out with the tea, allowing filtered tea without leaves to flow through into the tea cup below.
They can be made of silver, stainless steel, china, plastic or bamboo.
Some are designed to be pseudo tea infusers: they will actually rest on the rim of your cup or mug, but are deep enough so that they’ll be in the water. You pour the hot water through them, letting the water in the cup come up to submerge them, and then let infuse for the desired strength of tea before removing the strainer entirely.
Some metal ones come with stands (aka “dripping trays” in the trade) for setting them on tables.
Make sure bamboo ones are dry before putting them away.
For the more mystically-minded amongst us, the downside of tea strainers is: no tea leaves in the cup for fortune-telling later.