There were a couple of problems with Firefox 51 that prompted Mozilla to push out another new version yesterday. Firefox 51.0.1 resolves the two problems, one of which was related to the new multiprocess features.
Firefox itself seems to take a few days to notice new versions. Click the ‘hamburger’ menu button at the top right, then click the question mark icon, then click ‘About Firefox’ to see the version you’re running. In my experience, Firefox will usually say ‘Firefox is up to date’ until a couple of days after a new release becomes available. This is potentially confusing, but Mozilla doesn’t seem to understand that.
If you don’t want to wait for Firefox to notice the new version, you’ll have to download it directly from Mozilla.