**In the Forgotten Realms, Deities are those whom Ao has officially marked as deities.**

This answer is generally true for previous editions of Forgotten Realms. 
 It's possible that some changes may be made for 5th edition, though the Forgotten Realms is generally pretty good about maintaining continuity (including various cataclysms to explain edition changes).

Ao is the Overseer of the Forgotten Realms, and can raise, lower, or modify divinities at will, granting or removing portfolios.  He has full control over what portfolios are held by what beings, both through direct intervention and through making rules about how portfolios interact.  The essence of a divinity for the forgotten realms is in the possession of a divine portfolio.

Portfolios are generally accepted as being necessary in order to maintain persistent, stable cults.  It is possible to acquire a cult temporarily by just convincing people, but those don't generally last (unless Ao chooses to recognize the work by bestowing you a portfolio).  Deities are able to sense significant events that happen with respect to their portfolio, are able to pay particular attention to these events once aware of them, and have some degree of ability to directly influence their portfolios.