This is a type of tea sets used in Japan. Actually, the set in the pictuer has been handed down from my late gramdma.
It includes a teapot with no-handle called Hohin (literal. a treasure pot), two small teacups, and Yuzamashi (literal. to cool hot water), which is a temporary vessel for adjusting temperatures of hot water.
Obviously, if you prepare black tea using Hohin, you would get burnt because it has no handle. You should remember it!
Hohin is used for Gyokuro and high-quality Sencha, both of which are characterized by plenty of umami. In order to take great advantage of the character, lower-temperature hot water is a must. Infusing at too high a temperature extracts catechin (astringency ingredient) together with theanine (umami ingredient). Therefore, boiling water is not appropriate for preparing Gyokuro and high-quality Sencha.
This explains why Hohin won’t hurt you, creating "treasure" for you instead, doesn't it?
*Umami (Wikipedia) : http://en.wikipedia.org/wiki/Umami