It is the same as in algebra, if you have a variable, but not enough information to solve for that variable, it is unknown. For example, when you turn the power on to a sequential device, you don't know if it will come up as the value 1 or a 0. So we say that the value 'x' represents the potential to be either 1 or a 0. The we can let the Boolean logic propagate that value out to an observable output, or not. In verification, we want to make sure the design will eventually turn the unknown to a known value. For example (x & 0) = 0, (x | 1) = 1. This can be done in simulation or using formal tools.
An 'x' is also used to specify an unspecified input. Meaning that we want the synthesis tool to generate logic assuming that an input could be either 1 or 0.