Welcome Karen1992,
These topics have to do with convergence (or 'correctness') of the solution, which in HFSS for Driven simulations is evaluated on the basis of the scattering parameters observed at each port.
HFSS uses adaptive meshing, which is to say that it sets up an initial mesh, solves the fields, and then re-meshes based on where the fields have a high concentration and/or gradient. Each re-meshing step is called an "adaptive pass". Importantly, at each step, the scattering parameters are evaluated at each port, and compared to the previous step. The difference between the two is called "delta S".
So, in order to make sure a simulation is correct, HFSS does adaptive passes until the delta S falls below a set threshold. HFSS also gives you a large degree of control over this process: you can set delta S to be whatever you want, and you can also tell it to do a maximum number of passes, such that the simulation will stop whether or not the scattering parameters have converged.
Hope this helps!