A Whisper command sends a message to all other watchers of a match, but not to either player. Whispering allows you to converse with other watchers without disturbing the players. It is common courtesy that remarks about players' actions be done with whispers, for example.
To whisper, start your chat with "/whisper ", for example:
/whisper That was a good
double...
Starting a chat message with a period is a shortcut for /whisper:
.That was a good double...
Note that you can also whisper in the Lobby, although it behaves just like regular chatting and goes to all the players in the Lobby (so it's rarely used).