Convergence tolerances apply to the % change in a function value from one iteration to the next, and are used to identify when a solution has converged. As soon as this % change value falls below the convergence tolerance, the solution has converged.
Tightening a convergence tolerance may improve the solution accuracy, but will increase analysis time and may lead to convergence problem warnings. Also, if the analysis is generating convergence problem warnings, try loosening the tolerance to assist the solver in completing the simulation.