Question

How are self-replicating molecules, such as those in the RNA world hypothesis, essential to how evolutionists believe life began on Earth

Answer 1

3. RNA molecules have been shown to be not only self-replicating, information carriers, but catalysts as well. Thus, in the "RNA world," the preexistence of enzymes (proteins) is not required, thus simplifying what might have been needed for life to begin.

http://answers.yahoo.com/question/index?qid=20120215124345AAXbADP

Answer 2

I'm guessing "evolutionists" means "evolutionary biologist" (i.e. biologists who specialise in evolution) here -- otherwise it just sounds weird. Imagine calling all physicists "gravitists" because they occasionally make use of quantum physics or Newton's theory of gravity.

Anyway, the self-replicating bit is important because it's one of the characteristics that makes living things actually alive. It also makes evolution possible: organisms with favourable traits are more likely to reproduce (in the early earth, it might be more accurate to say that molecules with favourable traits are more likely to self-replicate), and that can, over time, lead to significant changes to further adapt the organism/self-replicating molecule to its environment.