How does physics scattering experiments relate to real life? And what does the scientist gain from such experiments? I am having a hard time figuring the answer out. Please help.
Depending on how you define scattering, its not only scientists who do these experiments, it is you, especially your eye.
Most likely you are referring to things like Rutherford backscattering or what is done at CERN, DESY, LHC & Co.?
In the end, the entire world can be seen as particles that are getting scattered by each other. E.g. electrons on atomic nuclei, cosmic radiation (i.e. "weird" particles) on atoms, and sunlight (i.e. photons) on you.
Physicists like those individual scattering experiments because they allow to isolate and study one of those myriads of possible scattering events that happen all the time. In such controlled environments, they can compare theory with reality/experiment. E.g. suppose you have a theory on what an electron and a proton are, and how they behave. Then you just shoot one on the other (under various angles, with various energies, etc.) and look whether the results are according to theory (which is good) or not (which is likewise good as this will lead to an improved theory or even overthrow fundamental concepts, both are seen as scientific progress).
Without the understanding from such experiments things like a transistor would not have been possible. Without a transistor, you would not have an iPod/Pad, no Mac/PC, no internet, ...
Actually, the physicist Werner Heisenberg, in his later years, even tried to model a theory of everything based on nothing else but scattering (S-Matrix, where "S" stands for ...).