Fair use is a doctrine of US Copyright Law that allows a person to use parts of a copyright work for specific purposes. It used to be a defense for that use, but was made part of copyright law. It is section 107.
The specific use of a work is for criticism, comment, news reporting, teaching, scholarship, and research. There are four factors that are considered in determining fair use. These are the effect of the use on the commercial value of the work, the portion of the work used, the nature of the work, and the purpose and character of the use, whether commercial, educational or nonprofit.
The key element is that the work used must meet the criteria specified. For example copying a picture to illustrate an article without referring to the picture itself would not meet the fair use provision.
Copying a piece of commercial sheet music for teaching students to play an instrument may meet the use provision (teaching,education) but would have a substantial impact on the commercial value of the work and so may not meet the full conditions of fair use.