A summons is a request or order for someone to show up, especially for legal matters. You could get a summons to testify at a trial, for example.
When you summon someone, you're requesting the person to join you, essentially saying, "Come here!" Similarly, a summons asks for someone to appear. This could be a friendly request or invitation, like a summons to join some friends for a road trip, but the most common type of summons is official and legally binding. If you receive a summons to appear in court, you have to show up. Ignoring that kind of summons is a crime.