In the context of Guild Wars, Beta refers to a campaign before it has gone "live" (i.e. before it has been publicly sold at stores). It is the time period where people play on the servers that ArenaNet had provided in order to test the program itself for the company, and, in the case of a public beta, give players a taste of the game (in not always convenient bite sized weekend chunks once a month) in order to stir up sales. Past public Betas include the Beta Weekend Events, the Factions Preview Event and the Guild Wars Nightfall PvP Preview Event.
For more general information see: "Beta Version" on Wikipedia