Forward must problem explanation in compiler design
I typically think of must as meaning logical and.

In the case of available expressions, when you reach a join point, the expression in question is available at the join point if and only if the expression is available on all of the input edges to the join point.  That is: if the expression is available on the first input edge, and it is available on the second input edge, and it is available on the third input edge, etc.

There are other properties, such as "could be a null pointer" which are may properties instead of must properties.  May I think of as meaning logical or.