The usually nonsensical phrase must of comes from a mishearing of must’ve, the contraction of must have.
The error is surprisingly common and appears even in edited writing—for example:
[A] far cry from the days the journey must of taken in Harry Carter’s time. [Guardian]
One has to wonder how many drinks this man must of had to try and flirt with the wife of a 7-foot, heavily built monster of a man. [Los Angeles Times]
Kendall must of used his time wisely as his under-3 ERA is a vast improvement over the 12.46 ERA he had in the Gulf Coast League. [Bluefield Daily Telegraph]
Though these examples come from publications that are both online and in print, the error seems particularly common in web writing.
In rare instance, must of can make sense—for example:
Policy on Zimbabwe must of necessity be subservient to this greater goal. [The Age]
But most of the time, must of is just a misspelling of must’ve.