System messages are messages generated by Discord. Usually, you will see them when a new person joins. To change whether these appear, and where they appear, go into your server's settings, and go to the Overview tab. There will be a System Messages Channel setting, with a dropdown menu that lets you pick which channel these messages are sent to. The General channel should be selected by default, but you may want to send them somewhere else to reduce clutter.
Below this setting, you can toggle whether Discord sends a message at all when someone joins the server or boosts the server. Keeping these things turned on can help facilitate good first impressions, as existing server members may welcome new members into the community.