What is the meaning of the jurists' statement: "The congregant invokes blessings upon the Prophet, peace and blessings be upon him, to himself, if he hears his name mentioned in prayers or in the Friday sermon," and what is meant by "to himself"?

The meaning of "reciting Salah to himself" is to send blessings upon the Prophet, peace and blessings be upon him, silently, without vocalizing or raising one's voice, so as not to distract people or become preoccupied with that during the prayer. This is permissible for the congregant (ma'mum) upon hearing the mention of the Prophet, peace and blessings be upon him, in prayer or during the sermon, provided that it is done briefly and not excessively.