OEM stands for Original Equipment Manufacturer.

In the case of ink cartridges it means that the manufacturer of the printer also manufacturers the ink cartridge as well, eg An Epson cartridge for an Epson machine.

Since Epson, Canon, Brother, Xerox, Dell and most other brands all sell their printer as a loss leader (The printer is sold at a loss, and then they then use the cartridges to make their money back), it is possible for other companies to make compatible cartridges for their printers, which are generally a lot cheaper than OEM cartridges.