I am sure you have seen tea strainers in action during a Chinese tea brewing session. You may be using one yourself when you brew your tea at home.
When you are a teashop sampling tea, almost of these tea sessions will employ the use of a tea strainer. The tea is your teacup would be free of mini bits of tea leaves and you can examine and sample the tea 'in more detail'.
Most teashops would use a simple strainer as the one in the 1st pix. It is simple to use. The tea is poured through the strainer into a cha he (server) before the tea is poured out into the tea cups.
There are now more fanciful strainers. The 2nd pix show a bamboo strainer while the 3rd pix is simply a dried leaf. That leaf, I was told, is called a pu ti leaf. From Taiwan. You simply pour tea over the leaf into your tea server. The leaf stays 'strong' - it does not wobble or spill over when tea is poured through it. A marvellous conversation piece to have in a tea session.