Keplerian elements are the inputs to the SGP4 standard mathematical model of spacecraft orbits. They specify the size and shape of the orbit, and how the orbit is oriented with respect to the Earth at a particular moment in time. 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 the SGP4 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. This format is also known as Two Line Elements or TLE’s.
AMSAT (verbose) format elements for all satellites of interest to radio amateurs. Written with additional annotation of each numeric value in each element set.
Additionally, AMSAT maintains NASA (2-line) stripped of headers The format is similar to the NASA (2 line) format bulletins, but may be updated more frequently. For example, the International Space Station elements are updated at least once a day based on data from NASA’s Johnson Spaceflight Center. These data are used as input to the AMSAT Pass Predictions page.
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. TLE’s for selected spacecraft, updated 4-6 times a day.
Space-Track NORAD source for TLE’s 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 orbital elements.