Mutation is the driving force behind improving your units in CURE. Mutations occur during a match while reproducing a unit. When a mutation occurs your unit will potentially gain a new visual appearance and some changes to their stats.
Some special mutations will actually unlock new abilities or units. The stat changes will act like a buff to your unit. For example a unit could gain an additional 5 hp from a mutation. Mutations will pass on to the next generation.
So if one of your units gains a very powerful mutation you will most likely want to selectively breed that unit to gain more units with that mutation. Mutations can also stack giving you the potential to create very powerful units during the match if you are patient and lucky.