Red Temples are the places of worship in the religion of R'hllor, the Lord of Light, called "Red" because of the color's association with the god. They are occupied not only by Red Priests but also temple warriors as well as temple prostitutes of both sexes.
In the books
In the A Song of Ice and Fire novels, Red Temples are where Red Priests conduct their devotions every evening, lighting a fire and praying throughout the entire night for R'hllor to bring back the dawn. In places where belief in the Lord of Light is strong, Red Temples receive children and also also buy them to be raised as priests, warriors and temple prostitutes. Bought slave children are given the title of Slave of R'hllor and are often branded with flaming tattoos across their faces. Those raised as warriors to protect the temples are known as the Fiery Hand.
There are Red Temples in all of the Free Cities, some of the greatest being those in Lys and Volantis. The Red Temple in Volantis is massive, three times the size of the Great Sept of Baelor in King's Landing. There's also a Red Temple in Selhorys as well as a small one in Oldtown visited by sailors. Many religions are worshiped in Braavos, and while only a small minority follow R'hllor, the city does have a small Red Temple, alongside the temples to other religions.