Sector sounds like section, doesn't it? That's a good way to remember that a sector is a specific part of society or the economy, made up of similar elements — like the health care sector or the education sector.
Our most common use of the word sector refers to a society’s divisions. For example, our economy is divided into the private sector (privately-owned interests) and the public sector (government). Other than that, the word also has many technical applications in math and science. From the Latin verb secare, "to cut," sector was applied long ago to math as a section of a circle, which carried through to military language as "a circle around a headquarters."