Why is Dalton's law of partial pressure important?
Well, for a start it gives chemistry and physics teachers a rich source of questions and problems to ask their students in exams....
...and secondly it illustrates the kinetic-molecular theory of gases. We can treat gases, to a VERY GOOD APPROXIMATION, as individual particles whose interaction with other particles is NEGLIGIBLE, and whose measurable physical properties for a given volume, temperature, and pressure are amenable to analysis by simple(?) Newtonian physics.