This is how the Past Tense is formed. Example: i listen to- eu ascult in Present Tense and i listened-am ascultat. ''Le avem'' would mean ''we have them'' but in this sentence we want to say ''we showed to them our new home'' which is an action that refers to past, so we need to use the past test form of the verb ''a arata''.
This is called the Compound Perfect Indicative tense, and to form it you use the following structure: (eu) am/ (tu) ai / (el/ea) a / (noi) am / (voi) ați / (ei/ele) au + past participle. For example, the past participle of "a lucra" is lucrat, so you can say "(el/ea) a lucrat" = he/she worked, "noi am lucrat" = we worked, etc.
Hope this helps! :)