It allows us to resolve structures on very small scales and also to set up conditions where new types of particles can be produced and their properties studied. Higher energy allows resolution of smaller structures. Hence to resolve small structures we need waves with smaller wavelength. No ordinary microscope can resolve objects that are small compared to the wavelength of visible light. Quantum mechanics tells us that particles also possess wave-like properties and that the wavelength shrinks as the energy grows.
Higher energy allows higher mass particles to be produced.
Consider the situation where an electron and a positron, each with energy E, travelling in opposite directions meet and annihilate. Now there is energy 2E available to make a new particle and its antiparticle pair, or a single new neutral particle. The only way we can study particles made from the heavier types of quarks is to produce them in accelerator-driven collisions. They are unstable and last for such a short time that there are none around us in ordinary matter. Some are produced in cosmic rays but their most significant role in nature was in the very early stages of the evolution of the universe, fractions of a second after the big bang.