A mine is a hole in the earth from which workers take valuable things: coal, diamonds, copper. It is also a bomb that explodes when it's touched, often buried in the earth.
When you think of mines, think of something beneath the surface or hidden. People mine for gold by sifting through water and rocks. West Virginia is famous for its coal mines. A mine field might describe a field laced with explosives — such as landmines. When people put these explosives in place, they're mining the land. Also, any dangerous situation can be called a mine field. Talking about sensitive subjects — like religion or race — is a verbal mine field for sure.