Keplerian elements are the inputs to a standard mathematical model of spacecraft orbits. 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. See also the tutorial on Keplerian elements and the explanation of the formats in detail used in these files.
If you really want to know the mathematics behind the elements, see Spacetrack Report No. 3 from NORAD (1.1 megabytes in PDF format). Most amateur radio tracking programs use a simplified version of the simplest model described in this report.
Current Kep Downloads
AMSAT publishes Keplerian elements weekly. Here are the current bulletins:
You can receive these bulletins regularly by e-mail by subscribing to the KEPS mailing list.
Keps in PDB Format
You can also download keps in PDB format suitable for PocketSat for PalmOS PDA.
Orbital State Vectors
Orbital State Vectors describe the Position and Velocity of spacecraft at some specified Epoch time. For further information, see the State Vector tutorial.
Space Shuttle Orbital Data
Space Shuttle orbital data is available during missions. Keplerian elements are available from NASA, CelesTrak and Space-Track (see links below.) The orbital state vectors for Space Shuttle missions are also available from NASA
You can find lots of Keplerian elements and related information on these other sites: