Chrome Canary is the version of Chrome that has the latest changes added by Google to their browser. Chrome has 4 release channels: /canary/ - /dev/ - /beta/ - /stable/.
Firefox Nightly is the equivalent of Chrome Canary for Firefox (they have /nightly/ - /beta/ - /release/), while Safari has Safari Technology Preview.
Using one of those versions, you are on the bleeding edge. The Google Canary name comes from those poor canaries used in coal mines. Wikipedia defines a canary like "something which warns of the coming of greater danger or trouble".
In short, those releases are put out there so developers and internal people at companies can try out the latest features which will later become part of the stable releases sent to the hundreds of millions of people using them.
Changes in browsers can take months to be part of the stable release, so it makes sense that you, as a developer, feel the need to try out the new features as they are introduced, rather than using them when they are widely available.
For example today I used Canary to test the Intl.RelativeTimeFormat and Intl.ListFormat features coming to ES2019. The Web is evolving at a fast pace.
Using /Chrome Beta/, /Firefox Developer Edition/ and the betas of macOS (Apple follows its OS release cycle for Safari) provides a safer experience, since the canary/nightly releases can sometimes break.
It's not mandatory and you can definitely do your job on the stable releases of browsers, too. It's just another tool at your disposal to do your work day after day.
If you like testing the latest features that browsers will only get in a few months before anyone else, JavaScript or the last CSS or Web Platform API stuff, this is where you can find them.
Those preview releases are not linked to the stable release on your computers, so you can test things without worrying that a nasty bug will cancel your bookmarks or break your main browser experience.
I definitely encourage you to use those browsers. Not as the day-to-day browser, as one day a broken release might crash or have weird side effects, but as a way to test and use the latest and greatest upcoming Web Platform features.