The Channel Master is the client designated as the master of a channel. The channel master is a client like any other, and special treatment and/or special behavior of channel masters should be decided upon by you, the Fusion developer, on a per-app basis.
If you want to take advantage of the channel master, design your events to handle both the case when you are the channel master and when you are not. Most events will be the same either way and you do not need to check this.
Be careful in your events: you are not your own peer, so you cannot select yourself if you use Peer > Select Channel Master. Check Channel > You are Channel Master condition is false before you try to select.
(You can switch to checking if a condition is false by right-clicking the condition and pressing Negate.)
There can be either one channel master or no channel master per channel, and in theory the server may change the channel master, but whether clients will understand that in practice is dubious.
When the channel master leaves, the channel may be set to close, kicking all other clients, or the channel may stay open, in which case by default there will simply be no channel master (even if the original master rejoins).