Simplified General Perturbations 4 (SGP4) is a mathematical model used to calculate the position of a satellite(s) relative to an Earth-centered co-ordinate system.
When given a two-line element (TLE) that describes the current position of a satellite, SGP4 can be used to calculate the future position of the satellite (this is called propagation).
SGP4 is a term commonly used to refer to both SGP4 (near satellite) and SDP4 (far satellite) models.
https://www.danrw.com/sgp4/ is a C++ SGP4/SDP4 library.
https://pypi.python.org/pypi/sgp4 is a Python SGP4 library.