A compound verb is a verb created with an auxiliary verb and another verb.
We use compound verbs to create all the tenses in English.
To understand better what compound verbs are, look at the below examples:
a) Most of the protestants were arrested shortly after. (Past Simple)
arrested—past participle of arrest
b) He will drive you to the airport after the dinner. (Future Simple)
c) The mother was looking lovingly at her child. (Past Continuous)
looking—present participle of look
d) I have been waiting here for half an hour! What happened?! (Present Perfect Continuos)
have and been—auxiliary verb
waiting—present participle of wait
e) By the next year, we will have been married for 30 years. (Future Perfect)
will and have—auxiliary verb
been and married—past participle of be and marry