How is reproduction important to animals life?

It depends how you define life

Most definitions of life do not have anything to do with reproduction. An infertile person (or other animal) cannot reproduce, so reproduction is not important to their life at all.

Some definitions of life include the ability to reproduce, so, using those definitions, reproduction is required for life.

to keep them alive and to make more of them.

Reproduction is important for the continuation of a species. All animals have a desire to reproduce. Some insects reproduce and then die, that is their only purpose in life.