Fish have been around for a long time. They first appear in the fossil record over half a billion years ago in the Cambrian. The earliest fish did not even have jaws, and jawless fishes are still with us today. Given all this time fish have had a lot of time to diversify. There are many lineages available from which new species can arise.
The second factor is that water covers roughly 3/4 of the Earth’s surface. This gives a lot of area for fish to live and creates many niches for fish to occupy. Bodies of water are also easily isolated by geological processes. Isolation and many available niches leads to lots of speciation. The African Rift Lakes are a perfect example. Each Lake was colonized by fish from a few lines which then rapidly diversified to fill each available niche. In the oceans, each island or reef forms an isolated area where species can diversify. Rivers and lakes form on the islands which can also be colonized by fish.
Finally, fish have a lot of reproductive strategies. Some, such as mouth brooding and bearing live young tend to favor isolation. Others broadcast millions of eggs into the plankton which allows for wide dispersal of the species.