This article is from the Photographic Lenses FAQ, by David Jacobson with numerous contributions by others.
SQF is an abbreviation for Subjective Quality Factor. SQF was developed by Ed Grainger of Eastman Kodak as an objective measurement that correlated well with subjective rankings of print quality. Somewhat simplified, it is just the MTF in the print (or referred to a designated print size or magnification) averaged from .5 to 2 cycles per mm. See the technical notes. One well-known popular magazine reports lens test results in terms of what they claim to be SQF, but they apparently use some other definition of SQF, despite showing Ed Grainger's picture and referring readers to his original SQF paper.