A particle collider is a type of accelerator.
An accelerator is the particle physics version of a microscope. We want to “see” such tiny objects, fundamental particles, that we will never ever see with our own eyes. To put things in perspective: a person with perfect eyesight can distinguish 40 µm wide objects. The diameter of an atom is, on average and using an approximate model, about 150 pm. A pm (picometer) is 10-12 m, while a µm (micrometer) is 10-6 m. In other words, atoms are about 10 million times smaller than what our best eyesight can distinguish.
It’s not about getting better reading glasses. We are not going to see anything that small, ever. So instead, we build microscopes. The irony is that the smaller the size we want to probe, the larger the microscope has to be. That’s pretty much how we end up with a 27km-circonference tunnel (the LHC at CERN), 175 m under Geneva and surrounding area.
Since we will not see the particles, no matter how hard we try, we have to infer what they are and how they behave by studying their interactions, with a controlled environment, or with each other. One of the ways to do the latter is to make them collide into each other at various speeds.
So, really, a particle collider is a giant, engineered car crash. That we use to examine the individual screws making up the car.