Here are some examples:
* "El amor de su vida": The love of his/her life.
* "Un recuerdo de su vida": A memory from his/her life.
* "El trabajo de su vida": The work of his/her life.
The phrase can refer to a specific event, a period of time, or even a general aspect of someone's life.
The gender of the noun or pronoun following "de su" will determine whether the translation is "his" or "her."