It is unclear whether the man's father has died and he will bury him immediately, or if the man wants to stay for a longer amount of time until his father dies so he can bury him then. The main point is that the man wants to do something else first before he follows Jesus.
Jesus does not mean literally that dead people will bury other dead people. Possible meanings of "the dead": 1) it is a metaphor for those who will soon die, or 2) it is a metaphor for those who do not follow Jesus and are spiritually dead. The main point is that a disciple must not let anything delay him from following Jesus. (See: [[rc://en/ta/man/translate/figs-metaphor]])