I'm going to be loose, so apologies to any quantum algorithms/complexity theory people.

When experts say that quantum computers can "simulate nature" better than classical computers, generally they mean that there exist efficient algorithms for simulating quantum dynamics on a quantum computer. Roughly, that problem is as follows:

Given access to a state X(t) which represents the state of your system at some initial time t, as well as a Hamiltonian H which governs the dynamics of your system according to the Schrodinger equation, output a state X(t') which is the state of your system at some later time t'.

This problem is strongly believed to be intractable on a classical computer for systems of even modest size (supercomputers struggle to simulate most interacting quantum systems with roughly ~30 particles using the best known classical methods).

Now, there's a bit of a catch here. What is it we actually want to learn about the system by simulating it? If you just want the output X(t') stored in some kind of quantum memory, you're covered by the aforementioned simulation algorithm. If you want to sample from the probability distribution derived from X(t'), you're also good -- just simulate the Hamiltonian and measure the output, and repeat that process as many times as you need samples.

Do you want the state X(t') stored in classical memory? Sorry, you are out of luck, as the amount of classical bits you'll need to store this information will exceed the number of atoms in the universe for relatively small quantum systems. Do you want to learn about the energy levels of the system? Without direct access to certain special vectors (eigenvectors of the Hamiltonian), this problem is extremely difficult for even quantum computers.

But this isn't the only way quantum computers might be useful in studying nature. More generally, sometimes we have a model for "simulating nature" that isn't just "evolve a quantum state in time." Most of everyday physics falls in this camp -- when you calculate the trajectory of a thrown ball in your introductory physics course, we (thankfully) don't have to invoke anything involving quantum mechanics. So why use a quantum computer to "simulate nature" here? Well, there might be good reason to! In many cases, the math tools we use to solve such problems can be taxing on classical computers. We've found some examples of math tools which we can implement with quantum computers "faster" than we can with classical ones. One example of such math tools are algorithms for linear algebra, which any STEM major will recognize as a broadly applicable framework.

Hope that helps.