Yes, Canvas gives students two ways to share video:
1. Recording video directly from their browser (or mobile device using the Canvas App)
2. Uploading a pre-recorded video from their computer.
Your next question may be, when and where can students share these videos?
On the one hand, you may want students to share videos with just the teacher as an Assignment Submission. If so, check out Instructor Guide: How do I create an online assignment? and the Student Guide: How do I submit a media file as an assignment submission?
On the other hand, you may want students to share videos with the class or their team members, for example, via Discussions. Pretty much anywhere students can access Canvas's Rich Content Editor they can record or upload and embed video! Even in a Quiz "essay" question. See How do I record a video using the Rich Content Editor as a student? or How do I upload a video using the Rich Content Editor as a student?
P.S. And as @ddaniels mentioned, Canvas Studio is a very cool "upgrade" for using media in Canvas.
This disucssion post is outdated and has been archived. Please use the Community question forums and official documentation for the most current and accurate information.