Two of the most common materials for soccer cleats are the following:Leather: There are many types of leather that are used for comfort, weight, durability, etc.
Three of the most common leathers used are full grain leather, kangaroo leather, and Goleo Calf Leather. There are unique properties to all three, but Kangaroo leather and the calf leather are used more frequently in high end cleats.
These Kangaroo and Calf leathers are much lighter than the full grain leather and tend to allow for a better feel on the ball.
As is the case with leather, in a game or practice in the rain, the cleats can deteriorate with becoming wet and then dry repeatedly unless treated with some kind of water resistant solution. Another difficulty with moisture when wearing leather cleats is that they can become heavy in wet conditions, losing that light weight feel.
Synthetic material: Many top brand companies will have their own particular name for the synthetic material they use, but the most common in the high end cleats is an enhanced Polyurethane material.
The unique properties of this synthetic material is that the cleats are much lighter cleats, flexible, and water resistant. They will be the same weight in wet or dry conditions and cosmetically are more difficult to scuff and scratch.
Depending on the type of synthetic material, you may feel stiff in the cleat and some do not mold as well as leather cleats do.