means A person whose job is to help others learn a subject, skill, or way of thinking.

from From Old English 'tǣcan,' to show or point out — the same root that gives us 'token,' something shown. So a teacher was first literally one who points: here, look, this way. The '-er' ending simply marks the doer, as in baker or writer. The shift from 'pointing out' to 'instructing' was already underway in early English, the finger becoming the lesson.