Meaning : Able to exist and perform in harmonious or agreeable combination.
Example :
A compatible married couple.
Her deeds were compatible with her ideology.
Meaning : Capable of being used with or connected to other devices or components without modification.
Incapable of being used with or connected to other devices or components without modification.
incompatibleMeaning : Capable of forming a homogeneous mixture that neither separates nor is altered by chemical interaction.