There are things that live in the water that are not fish. Crabs, for example, are crustaceans. (“Shellfish” are not actually fish at all – they are more closely related to insects and spiders.) This verse comes to prohibit eating certain small swarming things that live in the water, separate from the rules of kosher and non-kosher fish.
The Talmud in Makkos (16b) points out that eating a bug that lives in water violates four separate Biblical injunctions, based upon the number of times the Torah warns us about such things. This is why many people are careful to filter their water to remove tiny (but visible) crustaceans called copepods. (If something is truly invisible to the naked eye, it’s not problematic but if it can be seen, even if it appears to be a speck, it’s a problem. So amoebas and paramecia are okay, at least from a kashrus standpoint. More practically, yogurt with live cultures can be kosher.)
The reason is what we have stated before: you are what you eat, spiritually speaking. God warns us not to eat certain things that would have a metaphysically deleterious effect.
This mitzvah applies to both men and women in all times and places. It is discussed in the Talmud in tractate Makkos on page 16b. It is codified in the Shulchan Aruch in Yoreh Deah 84. It is #179 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #99 of the 194 negative mitzvos that can be fulfilled today as listed in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar. The Ramban (Nachmanides) feels that this verse does not specifically address swarming things in the water; it is a more general statement about all things we are prohibited from eating, lest they make us disgusting.