Its original author is Jos Vermaseren of Nikhef, the Dutch institute for subatomic physics.
It is widely used in the theoretical particle physics community, but it is not restricted to applications in this specific field.
[1] A text file containing would tell FORM to create an expression named myexpr, replace therein the symbol y by x, and print the result on the screen.
The result would be given like FORM was started in 1984 as a successor to Schoonschip, an algebra engine developed by M. Veltman.
It was initially coded in FORTRAN 77, but rewritten in C before the release of version 1.0 in 1989.