A side discussion is referred to as a separate discussion having outside the main conversation.
Example: Two students in a class are having a conversation in a classroom while the professor is explaining. Their side discussion will lead them into missing any important information that may have been said.
When they say "No side discussions", it is because they don't want smaller discussions as it may lead to some information being unheard. Side discussion often cause disruption in a meeting, which is also why they are frowned upon.