The U.T.S. is a point in a material where it begins to break down and tear.  "The straw that broke the camels back" is a very good analogy to this point at which the bonds in the material begin to break and the material becomes weaker.

In the stress-strain curve above, the U.T.S. is denoted as the "tensile strength".  As you can see by the stress-strain curve, at this point there will never be a greater amount of stress applied to the system.  In fact, the overall strength of the material will never be stronger due to the breakdown of the material and the breaking of bonds between the molecules or atoms.

Why important?

The U.T.S. is important because it can tell doctors and scientists at what force a material will deform.  Hence, it will give them a better idea of what material will work for a certain situation.  This is very important in the bone-metal interface.