Which subatomic particles are you asking about?

All of the technology you rely on, like your computer and your smartphone, depend at their core on semiconductors which would not be possible to manufacture in such small sizes and at such scales if we didn't have a very good understanding of the fundamental physics they depend on. The traces on chips these days are so small that quantum tunneling of electrons has become one of the limiting factors, and chips degrade because of electromigration.

Our best understanding and most accurate modeling of these issues comes from quantum theory. Quantum theory predicted the existence of certain particles, such as the Higgs boson. If we hadn't found the Higgs boson, it would have implications for the correctness of quantum theory, which in turn would imply that the models we use for the semiconductors in computers, smartphones, satellites etc. are wrong in some way.

In that case, figuring out the right model could help us understand and possibly overcome existing limitations.

Similarly, for understanding the universe, having a correct quantum theory makes a difference to our ability to use that theory in conjunction with other theories. If there are mistakes in quantum theory, it greatly reduces our chances of correctly combining or integrating quantum theory with other important theories such as general relativity.

In that sense, everything is connected. If you want to change the world in non-trivial ways, you have to understand it, and that's the goal of developing and testing scientific theories. Testing the existence of predicted particles is an important part of that. We test the predictions that the theories make in order to either confirm the theories, or find places that they fail and need work.

We apply the theories in extreme cases like the early Big Bang, and black holes, to see where they break down and to figure out whether the theories can be improved, or new theories developed. The result is that we end up with better theories that more accurately model and explain the behavior of the physical universe.

It's impossible to know where that will lead. Just 30 years ago, when a mobile phone weighed 11 pounds and could only be used to make voice calls, and personal computers had memories measured in kilobytes, today's smartphones were science fiction, literally.