The definition of Alpha varies from company to company. Generally, it is the point at which the game is mostly playable from start to finish. There might still be a few workarounds or gaps and all the assets might not be final, but the engine, user interface, and all other major subsystems are complete.
As you enter Alpha, the focus starts to shift from building to finishing, from creating to polishing. Now is the time to take a hard look at game features and content to decide whether any must be dropped in order to make the schedule. Now is when more testers come on to start ferreting out bugs . Now is the first time the game is seen and evaluated by people outside the development team.
The good news about Alpha is that it is the beginning of the end. The bad news is that reaching the end is seldom easy.