In the books
In the A Song of Ice and Fire novels, the tiger cloaks act as the city guard of Volantis, serving the ruling triarchs. Their name comes from the militant tiger party and they are fiercely proud of the green tiger marks tattooed on their cheeks. Their helms are fashioned to look like tiger masks and their gauntlets are covered with steel claws. Around half of the tiger cloaks are worshippers of R'hllor.
Tyrion Lannister encounters several tiger cloaks in Selhorys and wonders if they desire freedom and what they would do if Daenerys Targaryen granted it to them. One of them rubs his head and remarks that it is good luck to rub the head of a dwarf, though Tyrion is too started to resist.