The phrase 'suam domum vidit' translates to 'he/she saw his/her own house' in English, where 'suam' is a reflexive pronoun that indicates possession. Reflexive pronouns in Latin are used to show that the subject of the verb is also the object, emphasizing a connection between the two. This concept is crucial for understanding how actions relate back to the doer in both Latin grammar and the overall meaning of sentences.