Unity takes scripts written in C#, UnityScript (based on JavaScript), or Boo (based on Python), and compiles them into mono assemblies. Those assemblies + the 3d models, sounds, and textures required by your game are compressed into a .unity3d file that is loaded by their browser plugin. Since almost all of the game's logic is in managed mono assemblies it runs cross platform with very few platform specific quirks.

They've recently rewritten their plugin detection and installation code so that it is very easy to drop a block of javascript into a web page that shows Unity content if the user has the plugin, or other content (image, flash, video) if they don't. I believe their plugin supports all A-class browsers on Mac and Windows, and the plugin can be installed without restarting the browser.

One advantage of the Unity engine is that you can take a lot of off-the-shelf managed assemblies and include them in your project and call them from Unity code. But you have to be aware that these assemblies can really bloat the size of the .unity3d file.

Another advantage is that you can easily write components that expose tunable parameters that can be modified by non-technical people.

And yet another advantage is that a well written project can be ported to/from iPhone, Standalone, Android, Web, etc. in under a day. I've personally done iPhone to Web by just modifying my input handler and changing texture compression.

One big disadvantage is that since the application is running managed code it is not too difficult for a curious or malicious person to decompile the assemblies into completely readable code. So you need to think about what someone could do with that info (cheat in multiplayer, write bots, falsify high scores, etc.). It is possible to obfuscate your assemblies, but it isn't trivial to add this step to your build process.