What exactly are messages? Do you receive them from other players or is it only from mods?

Messages can be received from other Scratch users and moderators

Welcome to Scratch! You can receive a message because of many things:

• Someone followed you
  
• Someone loved or favourited one of your projects
  
• Someone commented on your profile, one of your projects or one of your forum topics
  
• Someone replied to your comment
  
• Someone invited you to join a studio
  
• There was some activity in one of the studios you've joined
  
• The Scratch Team (the “mods”) sent you an alert
  

Note: The “players” are not called like that on Scratch, we say “Scratchers” instead.

ajskateboarder wrote:

Messages can be received from other Scratch users and moderators

The OP might mean broadcasts
—
They basically have code run when you broadcast the message.

GIitchInTheMatrix wrote:

ajskateboarder wrote:

Messages can be received from other Scratch users and moderators

The OP might mean broadcasts
—
They basically have code run when you broadcast the message.

Here is a more detailed explanation of it

A broadcast is a message that is sent through the Scratch program, activating scripts with the matching hat blocks. Broadcasts are sent with the blocks Broadcast () and Broadcast () and Wait, and are received by the hat block When I Receive ().

Broadcasts allow scripts to continue into other sprites, as some values are different to different sprites. They can also be used to branch a single sending script into many receiving scripts, or to close many sending scripts into a single receiving script.

Broadcasts are useful in games and animations, as they trigger specific scripts. They are similar to events, which are scripts triggered when certain actions, like mouse moves or key presses, are performed.
Wiki

messages = https://en.scratch-wiki.info/wiki/Messages_and_Notifications

if you mean broadcasting,

messages = https://en.scratch-wiki.info/wiki/Broadcast