The tail serves many functions.
First, it helps regulate body temperature.
Second, it helps stabilize balance, which helps rats climb.
Third, the tail provides a defense mechanism. The tail can be
torn off in a process known as degloving; this is particularly
handy if a predator captures the rat by the tail. The tail will
pull off, allowing the rat a chance to escape. However, this is an
injury (meaning it is painful for the rat) and can lead to
infection. Degloving is one reason why you should NEVER pick your
rat up by the tail!