You may know that the speed of light is the fastest speed possible. That speed is 300,000,000 metres per second. When we talk of the speed of light we mean the speed that light travels in a vacuum, such as the airless void of outer space. Physicists call this speed "c".
When light travels through any material such as glass or air, it slows down slightly to a speed less than "c". Some high energy particles, such as the cosmic rays that you have been reading about can travel faster than this. When that happens the particles emit faint flashes of blue light known as Cerenkov radiation. This light is vaguely analogous to the sonic boom produced by aircraft that travel faster than the speed of sound.
It is important to remember that the cosmic rays are not travelling faster than "c". They are just travelling faster than light does after it has been slowed down by passing through a material.