1. boss: somebody whose job is to oversee and guide the work or activities of a group of other people
2. education main teacher of subject: a teacher or other school official who oversees the teaching and teachers of a single subject area
3. public administration elected official: an elected official in various local authorities such as townships and counties
4. U.K. education tutor for graduate: in some British universities, a teacher assigned to supervise the work of an individual student, especially research done by a graduate student
Supervisor is the only correct spelling of this word. It is sometimes misspelled with an -er ending, on the model of many other English words, notably adviser (which has a variant spelling in -or).
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