An original cartridge is manufactured by the same brand that made your printer. So an original cartridge for a HP printer is manufactured by HP.
A compatible cartridge is a cartridge manufactured by a different company for your printer. So a cartridge for a HP printer, but not made by HP.
Compatibles should be just as reliable as genuine cartridges, and are the best way to save money on your printing, without impacting print quality or the performance of your machine.