I haven't parsed all the numbers (though maybe I will in the future!), but let's just look at the US case (which accounts for over 1,000 of those tests).

Some US tests were about learning military effects of the weapons ("if we drop them on boats, what happens to the boats?"), which is important if you plan to use them in war, or are worried about someone using them on you.

A few of them were for non-weapon purposes, like seeing whether you can use them to dig big holes or basically "frack" natural gas with heavy shock waves.

A few of them were safety and reliability tests. In the later years of the program there were a bunch of these, where they would take a random warhead from the stockpile and set it off, just to see if it still worked how they expected it to. (Occasionally there were surprises — in 1963 they realized that 75% of their Polaris submarine warheads were likely to be duds due to a simple mechanical error.)

There were a few tests in the name of pure physics. Can we create an artificial radiation belt around the Earth? What are the limiting parameters for laser-driven nuclear fusion? Things like that.

But the vast majority of US weapons tests fall under the category of "weapons development." This is pretty vague, and it ranges from "let's test a totally new idea" to "let's see if our understanding of value X is correct." There was a lot of the first category in the early years of the program, when there was still a lot to learn. You can't design sophisticated weapons without knowing a lot about weapon physics, and weapon physics takes place in energy regimes that are just otherwise pretty inaccessible to experiment. (At the temperatures and pressures of the inside of an exploding nuclear weapon, dense metals act like fluids or gases. Temperatures can be similar to the insides of stars. This is just stuff that is inherently hard to test any other way. Not always impossible! But hard.)

The last major innovations in US weapons design were figured out in the early 1960s. After that, in the words of one weapons designer, it became something of "polishing a turd" exercise. You tweaked things to get a little better efficiency, a little better reliability. They found ways to improve the safety of the bombs without losing their usefulness (e.g., by developing shock- and heat-insensitive high explosives that won't go off unless you really want them to).

They also worked to refine their theoretical models. With a good theoretical model, you can do a huge amount of work without testing. The problem is, our models have never been able to fully simulate a nuclear weapon from first principles. This is because the operation of a nuclear weapon runs the entire physical gamut, from the atomic scale up to the destroying-cities scale. Even supercomputers can't do that perfectly. Our computer codes for simulating weapon outputs contain lots of little patches (called "knobs") that are basically corrections to the results learned from late-Cold War underground nuclear testing. "Ah, you'd think the neutron would do X, but it turns out it does Y." (I am just making that up. I don't know what these "knobs" look like. They are mega classified. I still think it's great they are called "knobs." They are considered "ad hoc" models that are not "science based" in the same way that pure theory is.)

Anyway. As you can imagine, a weapons designer in the Cold War was going to be able to find lots of ways to justify more testing, especially once it went underground and got out of the public mind. That's the story the labs will tell you: every test was about Science with a capital "S" and it was all about defense. Grand.

What other forces were at work? I wouldn't call it "dick waving" in the US context (there are a few tests on each side that are hard to justify from a scientific standpoint — Crossroads in the US and the Tsar Bomba in the USSR come to mind — but they are pretty rare). There was a sense that a vigorous nuclear testing program would enhance the nuclear arsenal, and perceptions of the nuclear arsenal. So that's a little dick-wavy. But the "dick waving" idea seems to imply that people in the political or military establishment were influencing the number of tests for international reasons. I don't see a lot of that when I look at the records.

What one does find, though, is that there were strong sociological reasons for testing. The scientists at the labs, for example, clearly got a lot out of the activity. For them it became a rite of passage. You didn't get ahead in the US labs unless your ideas made the ground rumble. Pull off a really clever stunt? Might be Director material, someday. (John Nuckolls, a young designer at Livermore, came up with a very radical design in a record amount of time in 1962, and its success paved the way for a new generation of warheads. He did eventually become lab director.)

Basically what the testing did was give the scientists an incentive to find justifications for an experimental physics program on an unprecedented scale. It gave them a political justification for it, too. So you get sort of a feedback system where the scientists say they always need more tests, and the politicians support it because it makes everyone look like they care about national security.

Until one day the politicians (much to the chagrin of many of the lab scientists) decide to stop testing. And then everything gets a little more problematic. Until the politicians promise the scientists some big fancy new facilities (DAHRT, NIF) that allow them to do "testing-lite" — getting the results from experiments without actually testing nukes. Then the lab guys signed on.

Anyway. There is a lot of generalization above. My favorite peering into the world of the scientists and their test culture is Hugh Gusterson, Nuclear Rites, an anthropological view of the Livermore lab at the end of the Cold War. I don't mean to trivialize the science. It was real science most of the time, proposed by serious scientists. But it's one of those "if the only tool you have is a hammer, every problem looks like a nail" sort of things.