What is the function of the lizards tail

If a predator is chasing the lizard and catches them by the tail, it actually breaks off as a defense mechanism. It grows back so it looks normal, and so it can live a normal life. Like someone said before, it is also for balance. However, I do not know how long it takes to grow back, but I would not say too long, because an open wound left in the open air for a long period of time would risk infection. I would guess about 2 or 3 weeks growth time.

along with what everyone says
a tail can also save a lizards life, some lizards as they are being chased by a hunter and this 'hunter' catches the tail the tail detaches itself and later grows back

The tail of lizards is an important element for locomotion & balance. These animals move by mean of undulations of their entire body axis (vertebral column), & the motions of the tail counteract those of the trunk.
In addition, most lizards r capable of autotomy, that is, they can shed their tail at need, usually when threatened by a predator or in other highly stressful conditions, & then grow a new tail.
This is achieved by means of special intravertebral fracture planes, that is, each of the autotomic vertebrae has a weak transversal plane through which it can break into two pieces. In addition, the tail muscles of the autotomic region r arranged in small ''brick-like'' packages that can become separated without much tissue damage; the blood vessels in the area also have the ability of closing & clotting rapidly so as to avoid excess blood loss.
Under stressful conditions, the animal will experience reflex contraction of those specialized muscles & a fragment of the tail will become separated from the rest of the body. This fragment continues to thrash & move for some minutes after autotomy, thus attracting the would-be predator while the lizard escapes to safety.
Afterwards, a new tail will grow (this can take several months, according to the metabolic rate & general conditions of the individual); but this new tail does not have real vertebrae, only a rod-like support tissue. It usually has a blunt tip & different color/texture from the original tail.
There r _no_ autotomic vertebrae inside this new stump; therefore, the next autotomy will have to occur in vertebrae that r closer to the trunk. The number of these special vertebrae is limited, so the amount of autotomies is also limited.
Autotomy is obviously advantageous as a means of escape. However, tail loss also implies a disadvantage, basically because: 1) as other users have answered, many lizards store fat supplies in the tail (although normally the basal part of the tail is not autotomic); 2)''growing back'' a new tail requires more energetic resources that might have been used for other purposes; 3)until the new tail grows, locomotion may be somewhat impaired.
And I am leaving out other (e.g. social communication) uses of the tail.
Interestingly, the tail wo not grow back if the severance does not occur at the special fracture planes.

Lizard tails serve numerous purposes. They aide in balance & locomotion, maintain social status, & r a body area for fat storage. The tail provides a food source during periods of starvation & reproduction. Tail-less lizards also seem to lose social status; for example tail-less males r less likely to find a mate, & tail-less adolescents find it more difficult to acquire a home range. Losing the tail has serious consequences & does put the lizard in a more threatened state of existence. If they live long enough, some lizards can grow back their tail.

thats what you call renewable food

for balance

the lizards tail balences it while running. it also stores most of it is fat in it is tail.