What does the "maxiters" solver option do?

I have a question. How I can simulate/solve the ODE i.e. for quite long simulation duration? I.e. 2000s.

I ask, because I got this warning as well. Not during the optimization, but later when I just solved the ODE for a long tspan. I tried to increase the maxiter parameter, but then the solving didn´t finish (I let it run in the background for some hours). I could imagine, that simply stacking smaller solvings would work, but I think there is perhaps a more comfortable way, which I don´t know.

I got the warning in the context of the problem, which is described under the following link.