The word amateur has at least two connotations. In the first, more widely used manner, it means someone performing some task without pay, in contrast to a "professional" who would be paid for the same task. In this sense, labeling someone an "amateur" can have a negative connotation. For example, amateur athletes in sports such as baseball or football would not be regarded as having ability on par with professional athletes in those sports.
Where this can be interesting is in the case of the Olympic Games. Most Olympic events required that the athletes be amateurs, or non-professionals. To receive pay to perform the sport could have disqualified an athlete from an event, as in the case of Jim Thorpe. Such regulations are now nonexistent for all Olympic sports with the exception of boxing.
Also in the areas of computer programming and open source, as well as astronomy and ornithology, many amateurs make very meaningful contributions equivalent to or exceeding those of the professionals. To many, description as an amateur is losing its negative meaning, and actually carries a badge of honor.
The other, perhaps somewhat obsolescent usage, stems from the French form of the Latin root of the word meaning a "lover of". (See amateurism.) In this sense, retaining its French inflexion ("am-a-tEUR"), an amateur may be as competent as a paid professional, yet is motivated by a love or passion for the activity, like a connoisseur. In the 17th and 18th centuries virtuoso had similar connotations of passionate involvement.