How did redi and pasteur's experiment contribute to the current scientific understanding of how life on earth began?

Their experiments rejected  the hypothesis of spontaneous generation.

Redi was the first one who showed with his experiment that the theory of spontaneous generation could not be supported. His experiment with three glass jars with meat (the first was open, the second was covered with a loos netting, and the third was completely closed) showed that the meat cannot produce flies and maggots by itself (meat could not transform into flies as proposed in the theory of spontaneous generation).

Paster approved that cells cannot be generated spontaneously. Pasteur did the experiment with swan-necked flasks and straight-necked flasks (control). Microorganisms fell into the straight-necked flask entering the broth from the surrounding air, so he found living organisms only in that control flask.  

in 1859, charles darwin set out his theory of evolution by natural selection as an explanation for adaptation and speciation. he defined natural selection as the "principle by which each slight variation [of a trait], if useful, is preserved".