Star notes are used by the BEP (Bureau of Engraving and Printing) to replace misprinted/damaged currency before it goes into circulation. These replacement notes are printed just like normal notes, except there is a star printed in the serial number. On Federal Reserve Notes, the star is where the block letter normally is (the last letter of the serial number). On Legal Tender notes and Silver Certificates, the star is where the prefix normally is (the first letter of the serial number).
Star notes are printed in what are called "runs." For the current printing systems used by the BEP, the maximum run size for star notes is 3.2 million notes (100,000 32-note sheets). Sometimes, this many notes are not needed, in which case less are printed. If a partial run is printed, the next run will start at the next closest multiple of 3.2 million. Star notes get their rarity from the quantity printed and released into circulation. Generally, collectors consider runs of 640,000 notes or less to be rare. Many times, collectors refer to star notes by their run number. This is determined by the number range that the star note's serial number fits into. Here are the ranges for the run numbers:
These star notes are more common than sheet notes - the are printed in greater quantity. They are printed, cut, and put into straps, just like regular currency. If a strap of cut notes are found to have a damaged/misprinted note, the strap is destroyed and replaced with a strap of these star notes. This makes it possible to find multiple of these star notes at a time.
These are the rarer of the two types of star notes. They tend to be printed in quantities of 640,000 notes or less. If a sheet of damaged/misprinted notes are discovered before the cutting process, it is replaced with a sheet of stars. This means it is extremely unlikely to find more than two of these notes at a time.
If you want to find the rarity of a star note, you need to find the production values for that run and FRB. I have two references on my site for series 1976 to the present - the Star Note Lookup and production tables: $1, $2, $5, $10, $20, $50, $100.