Value of mathematical models in biology
This question is broad.

There are plenty of uses of mathematical modelling in biology.

Wikipedia

You may want to read the wikipedia article: Mathematical and Theoretical Biology.

Books

There are tons of books on theoretical biology. I am personally working in the field of population genetics, a field where much of the theory has been expressed mathematically. Here are book recommendations for this particular field.

On Biology.SE

We have a tag for mathematical-models (you used it in your post). You may want to see what kind of posts are tagged for mathematical-models.

To repeat @fileunderwater's comment, What physics knowledge can be applied to biology of organisms and ecosystems and When are population dynamics models useful? are examples of posts you may want to read.

What prevents predator overpopulation? will give you an example of an easy and classical mathematical model to describe population dynamics of predators and preys.



Personal historical/philosophical note: At some point physicists have started to describe the laws of nature with mathematical expressions and at that time many physicists didn't quite like the idea that physics could be described by math. Biology has gone through the same phase but much later. Early mathematical biologists developed the modern science of statistics (Francis Galton, Karl Pearson, Ronald Fisher). Biologists used existing mathematical tools such as diffusion processes (Kimura). Note that part of the work in the field of diffusion equations have been done by physicist (Einstein solved the 2D equations for diffusion processes). Note also that the dynamic of diffusion processes called brownian motion have been named after a biologist. Today, biology produces massive amount of data that require good computational skills to treat. The time when biologists had only to know how to recognize species is over, now there are few biologists left that aren't able to code in at least one programming language.