For what reason(s) did Miller and Urey decide to perform their experiment?

Question

..and how did it contribute to the hypothesis about the orgin of life

Answer 1

They thought they had a good idea how the early Earth's atmosphere must have been composed.  They attempted to reproduce it, and simulated some lightning.

It turns out that they had much of the atmosphere wrong.  But the idea that you could produce amino acids so easily has sparked the imagination.

People are still working on the problem.  So there's no way to know how the story turns out.

Answer 2

You'd need to ask them, read biographies, or read their writings to try to discern their motives.  Its direct objective was to try to answer a tiny part of the question, "Could life have happened by accident?"  It's probably the best known experiment related to the abiogenesis question.