Originally, a man's light jacket, often single-breasted, that is not part of a standard suit, specifically because the jacket is a different color from the pants. It is often part of a uniform, and in the case of school uniforms a blazer may be striped in the school colors. As you might imagine, while blazers are socially acceptable in the proper context, they are often a bit on the ugly or gaudy side.
The term blazer is comparatively recent, first appearing as a bit of British university slang in 1880. It comes from the 'blazing' red of the flannel jackets worn by the St. John's College, Cambridge boating club, and was quickly generalized to any bright jacket worth by college students.
These days most blazers are black, grey, or dark blue, and are fairly stolid garments. They are distinguished from a sportcoat, if at all, by a less formal cut and bright metal buttons. They are also no longer just a men's jacket, and most blazing blazers seen today are worn by women.