if two people or things are at variance with each other, they do not agree or are very different:
Tradition and culture are often at variance with the needs of modern living.
2 [uncountable and countable] formal
the amount by which two or more things are different or by which they change:
a price variance of 5%
3 [countable] law
the official permission to do something different from what is normally allowed:
The developer requested a variance to build a shopping center on the east side of town.