"Mein Boss hat mich gestern seiner Frau vorgestellt!"
Translation:My boss yesterday introduced me to his wife!
Several times 'hat' is in German sentences but not in English. What is it's purpose?
It's because present perfect tense is greatly preferred over simple past tense in spoken German. If this sentence would use simple past tense like the English translation, it would be "Mein Boss stellte mich gestern seiner Frau vor". However, simple past tense is almost exclusively used in literature (in the narration, usually not in the dialogue).
I agree. Maybe I wanna add here that this how the German perfect tense is often constructed: the conjugated auxilliary verb haben + past particple. That works pretty much like the English perfect tense (<-- has + past participle). Cf. https://www.germanveryeasy.com/perfekt
DUO assumes that using Present Perfect in English translation of this sentence is a mistake. I am not a native English speaker. Is it really a mistake to use Present Perfect here?