Dark matter means there’s a gravitational effect that we can see, but the source is in a spot where we see nothing, so we guess that there has to be something that we can’t see - that doesn’t emit any radiation, starting with light / heat. The lack of electromagnetic radiation is why it’s dark, and the gravitational effect is why it has to be matter - as in something heavy, particles that have a gravitational effect.

We know spots where “matter that we can’t see” should be. The biggest classic example is the bullet cluster, where most of the gravitational effect is outside of the light we see. What we can make progress on is take a list and strike out what it isn’t. We look at some kind of particle we know about, and we check if that could have the effect we see. If it can’t, we shorten the list of what dark matter might be. There’s been a few times along the decades where people said “this time we might have found the one” but so far, we keep shortening the list. The day we say “this time we actually detected something” is the day it won’t be called “dark” anymore, since “dark” is literally because we can’t detect anything coming out of it. Either we’re not looking hard enough to see the radiations we could expect from known matter (except we should be seeing something already with our current tech), or it emits something we can’t see, new types of emissions that we don’t know about. If we ever find a new type of matter that doesn’t emit anything we can see, then it can still be called dark, until we learn to detect it.

It’s possible that our understanding of gravity is wrong and the source of the gravity we see comes from something else in another spot, and the spot we’re looking at doesn’t have any matter we can’t see; but everytime we find something new about gravity, it keeps reinforcing our understanding of it and decreasing the odds that we’re wrong about it and dark matter doesn’t exist. And the theories about gravity that come up to fit the effect we see always create other problems by failing to explain other observations, whereas the current gravity theory does explain everything else. The window for “our current models of gravity are wrong” just keeps getting tighter and harder to justify with every observation that keeps getting more accurate.