A client can move between one basic service set and another by roaming between access points.
The client continuously checks the connection quality to the wireless access point that is connected too. If the signal degrades too much, the client will search for a new access point to roam too that can offer a better signal.
The client searches for new access points by scanning available channels and sending probe requests to discover available wireless access points. If the client finds an access point, it will try re-associate with it.
The client chooses a re-association rather than a new association request as it wants to preserve its original association status.
Roaming can happen with more than two access points, the client will continue to move from one to another where the signal quality on the new offering is better.