I have came across this in many places so I assume it’s a well known thing cause many people use it.

It is mentioned on page 50 of Burhanul Mutah: “One who performs Mutah once gets the rank of Hasan. One who performs twice gets the rank of Husain. One who performs thrice gets the rank of Ali and one who performs Mutah four times gets the rank of the Holy Prophet (S).”

What “rank” is this talking about? What is the deeper meaning of this statement?

There is no source for this hadith. Some scholars have said it’s a fabricated hadith