Explain the role of mutations in the biological evolution of species.

Mutations can be beneficial, neutral, or harmful. They are also random. The other thing to note is that only mutations in cells that are passed onto the next generation are important to evolution of the species. 

Evolution absolutely depends on mutations because this is the only way that new alleles and new regulatory regions (that control the expression of alleles) can happen.

Neutral mutations don't mean much. However, harmful (deleterious) or beneficial (good) mutations matter greatly. 

If a mutation is deleterious, then the resulting offspring likely will die and that mutation will not be passed onto the next generation. On the other hand, beneficial mutations could possibly result in new structures or new functions for proteins that are helpful to the survival of the organism. Natural selection (survival of the fittest) would then rule in favor of these traits and will therefore be passed down into the next generation. Overtime, if these traits are heavily favored, they will become more predominant in the population.