It doesn't need to be web-based, of course. This isn't anything you couldn't do before — it's just much easier to setup and has fewer points to get wrong (ever see a jump server whose owner forgot to change the port 22 0.0.0.0/0 allow rule?). It's especially nice because it works for everyone in every context without needing anything setup so you can safely use it for examples, training, someone working with a loaner machine, etc. even if you normally work with a custom configuration.
I have worked in places which say, "no code on laptops! You get a remote machine, all code must live here"
Same security advantages, but you get way more customize-ability -- choose a terminal app, font, fullscreen or many windows, and so on.