The 'max_evals' parameter in Hyperopt's fmin function is used to set the maximum number of trials (evaluations of the objective function) for the optimization process. It directly affects the exploration of the hyperparameter space by determining how many different hyperparameter combinations will be tested. A higher 'max_evals' value allows for more extensive exploration, potentially leading to better hyperparameter combinations, but also increases the computational cost. A lower value reduces the exploration but can save computational resources.