A tyre casing is the structural section of the tyre which the treaded area is attached to.
In some cases the casing of an old tyre is made into a new tyre by remoulding a new treaded area onto an old used tyre casing, although remoulds are not as common these days as they seem to suffer from defects more then a budget new.
It is also common for scrap tyres to be referred to as old casings.