She wants kids, he doesn't? She's married to him, he's married to his work? That's incompatibility right there: the inability of two sides to exist in a harmonious relationship with each other because of their different outlooks and beliefs.
It's not just relationships between people that are characterized by incompatibility, though that's the most common use of the term. Different objects and ideas can be, too. Being tone deaf is incompatible with being a good singer, for example, and if anyone's ever tried to run a Mac program on a PC they know all about the incompatibility of different computer systems.