Making an alias to something is basically making a "link" back to that file, much like a bookmark is a link back to a certain web page.
I find aliases useful for making "Dock menus" -- I simply create a folder named, say, "Applications," and then I put aliases to all my applications in that folder. Drag the folder to the Dock, and you've got a right-clickable menu that'll let you launch an application in 2 clicks. I've got a ton of applications I use on a daily basis, so keeping all of them in the Dock is unrealistic. Put aliases to the lesser used ones in a folder, and you don't have to go hunting on the hard drive.
They're also helpful for server volumes, as instead of doing the tedious command-K, select server, username, password, you can simply make an alias to a server volume, double-click it and it should mount.
Aliases are superior to duplicating the original file because aliases take up extremely little space on the hard drive... if you wanted a double-clickable folder on your desktop for your music, you wouldn't keep a copy in your iTunes music folder and another copy on your desktop (a HUGE waste of space, especially if you've got gigabytes of music) -- you'd simply make an alias to the music folder and keep the alias on your desktop.
Aliases even work like regular folders. If you've got an alias to some folder buried deep in your hard drive (or on a secondary hard drive, or on a FireWire drive, etc.), then you don't have to go hunting for that folder to put files in or take 'em out -- simply drag and drop on the alias.
"Create Archive" makes a standards-compliant .ZIP archive file. .ZIP has been the de-facto standard for compressing files on Windows for years, and is a decent replacement for the old StuffIt compression we used on our Macs in the past.
besides using the contextual menu (control-click, select "make alias") you can also hold down the APPLE and OPTION keys together as you drag... notice how the cursor changes to have a little curved arrow? that represents "alias", versus the plus sign for "copy" (just the OPTION key).
On Tiger I've noticed that you can also just hold down the CONTROL key as you drag to make an alias. First time I've noticed that behavior.