This happens early in embryonic development in females, where one of the two X-Chromosomes is randomly (and permanently) inactivated, as you said, in cells other than egg cells.
This phenomonon is actually called X-Inactivation.
X-Inactivation make sure that females, just like males, have a single functional copy of the X Chromosome in each and every one of their cells in their body.
Glad I could help, byee now