It’s up to the client on how to render them. Most videos I encounter in Lemmy are linked from outside sources or are on YouTube.
Lemmy-UI has no or limited support for anything but images.
Tesseract is on the other end of the spectrum and supports pretty much every kind of media.
Photon supports GIFs and native (mp4, webm) videos.
Other UIs and mobile apps, I haven’t kept as up-to-date on but are typically somewhere between Lemmy-UI and Photon’s level of media support.
Edit: In addition to what clients support, it’s also up to each instance admin to define what media they allow to be uploaded. Among the possible configuration options are:
Whether to allow any media uploads at all
The max size of the media they’ll allow users to upload
Whether to allow videos or just static images
Whether to convert videos to GIFs or static images
Whether the media subsystem (pict-rs) can process the upload before the upload request times out. I think that’s 10 seconds which limits direct uploads to short videos.
Like others have said, hosting videos is expensive both in areas of storage and bandwidth. Most Lemmy instances are run by volunteers at their cost or operate solely on donations. Admins typically ask users to host those off-server (Imgur, YouTube, Catbox, etc) and restrict what can be uploaded directly to reasonable limits.