What makes animal to continually reproduce?
Why organisms reproduce

If they didn't reproduce, they would die out.

More concretely, suppose an animal is born with a mutation that removes the desire to reproduce.  That animal will not have any offspring, so its genes will not be passed on to the next generation.  When that animal dies, that mutation will die with it.

Why some organisms reproduce a lot

Different animals or other organisms have differing strategies for reproduction, based on their ecology.  Some animals, like the Surinam toad, try to have a lot of offspring with relatively little "investment" (of energy, time, effort, etc.) in each one.  Many of the offspring will die, but enough will survive that the organism's genes can persist.  Other animals, like elephants, only have a few offspring but spend a lot of effort in making sure those few offspring survive.

You can read more about this in the Wikipedia article on life history theory.