Keplerian elements are the inputs to a standard mathematical model of spacecraft orbits.They specify the shape of the orbit, and how the orbit is oriented with respect to the Earth. With the “Keps”, the correct time, and your station location, you can compute when the satellite will be in view and where to point your antennas.
If you really want to know the mathematics behind the elements, see
Spacetrack Report No. 3 from NORAD. Most amateur radio tracking programs use a simplified version of the simplest model described in this report.
AMSAT publishes Keplerian elements weekly. Objects on these lists are chosen based on their interest to radio amateurs. Here are the current bulletins:
NASA (2-line) format elements for all satellites of interest to radio amateurs. Contains brief information on the format.
NASA (2-line) stripped of headers Similar to the NASA (2-line) but with no extra verbiage.
AMSAT (verbose) format elements for all satellites of interest to radio amateurs. Written in human readable format.
You can find lots of Keplerian elements and related information on these other sites, including NOAA weather, Iridium, and all other unclassified satellites not strictly of interest to the amateur radio community:
CelesTrak by T.S. Kelso. Keplerians for selected spacecraft, updated 4-6 times a day.
Space-Track NORAD source for Keplerians going back to Sputnik 1. Requires a free account for access. Current satellites updated 4-6 times a day.
Orbitessera by Ken Ernandes. General information on Keplerians.