The pallium (dim: palliolum) was the Roman cloak that was worn by both men and women (called a palla in the latter case). It was a rectangular piece of cloth, square in form, as was the himation in ancient Greece. It is not to be confused with the pallium, in the Catholic Church, which is related to the omophor.
The pallium, which was considered at first to be exclusively Greek and despised by Romans, was taken into favour by ordinary people, philosophers, and pedagogues, and eventually replaced the toga on the 2nd century BC.
The material of this cloak was usually made of woolflax or cotton, but for the higher classes it could me made of silk with the use of gold threads and embroideries.
The garment varied in fineness, colour and ornament. It could be white, purple red (purpurea from murex), black yellow, blue, pale green, etc.
It could be used as a blanket, to spread over beds or cover the body during sleep.
In Tertullian's mind, the pallium, which he adopted a toga ad pallium, was the cloak of philosophers and Christians.