An open beta is a beta-level release of a game which its maker exposes to the outside world. The reasons for doing this are to get player feedback early, to use the players as a test group to find bugs, and finally to create a participatory community around the game that carries its makreting story.
Open betas have become more popular and possible in the online age of cloud computing, social networks and cheap data. Nowadays a small developer can maintain a conversation with millions of fans and involve them in the process in a way that they could only dream of twenty years ago.
However open betas do not suit all markets equally. Muggles, for example, just expect a game to work and have no interest in particpating in its creation. Consoles have strong barriers between the developer and consumer which prevent effective communication and regular releases of game updates, both of which are necessary for an open beta to work.