"Freemium" is a portmanteau of free ("provided without payment") and premium ("high quality" or "an extra bonus"). It is used as an adjective.
A service described as "freemium" or as having a "freemium business model" provides its most basic services for free, but entices customers to upgrade to a paid subscription. Customers usually receive special benefits with their paid subscription that somehow enhance the "basic" service they previously received.
This may be described as a sort of mild bait-and-switch: the service provider reels in the customer with the free service, but then attempts to convert that free customer into a paying customer by selling them on further services.
Internet games often employ a "freemium" business model. Players may make an account and play for free, but they may receive in-game bonuses (money, powers, equipment, etc) in exchange for real-world currency.
In persistent multiplayer games such as Dead Awaken, players who pay for in-game money and equipment enjoy a substantial competitive advantage over non-paying players. In single-player games, a player who pays for extra in-game content is not buying a competitive advantage, but may simply wish to have more in-game money and power to enjoy during play time.
One game often described as freemium in this sense is Zynga's FarmVille:
Another sense of "freemium" is in the case of a community offering certain intangible benefits to members who donate money to keep the community as a whole afloat. Social news website Reddit recently appealed to its users for voluntary donations of any amount. Those who donated received public recognition in the form of a "trophy" on their user page, as well as a promise of possible unspecified benefits in the future. Some commentators described this as being a type of "freemium" service: