Hi there @JenniferWetzel ,
Welcome to the Instructure Community!
Once you create a group inside of a course and add a student to it, depending on the student's notification settings, they may or may not receive a notification that they were added as a member to a group. Depending on the course settings, students may or may not be able to create their own groups. If this is something you would like your students to have access to, I'd recommend that the check box in your course's settings isn't checked off, disallowing students from creating their own groups. By default, students can create their own groups.
When students are enrolled in those groups, they are able to create their own discussions, upload their own files, send out announcements and group messages, and even start a BigBlueButton conference, if they are permitted to (that is determined at the account-level).
In addition, I thought I'd provide you with a link to a guide that has some additional information about groups. https://community.canvaslms.com/t5/Canvas-Basics-Guide/What-are-Groups/ta-p/16
I hope this helps, please reach back out with any questions!
Best,
Noah