The standard Ubuntu Cd is a live CD - you can choose to boot from the CD drive in your BIOS options (when the computer starts up) and then run Ubuntu, without making any permanent changes to your computer. This is useful if you want to try Ubuntu out, see what it looks like, how it performs and whether your hardware and peripherals will be compatible. It will also install Ubuntu to your hard disk, or virtually (inside a Windows Operating System) using WUBI (so you can choose Ubuntu inside Windows just like it's a program).
The alternate installer is not a live CD. The installation process isn't as pretty - it uses a text-based installer. However it has more options to choose from when installing - you can install Ubuntu without a Desktop (so it's just a text console) and so on. It can also be used as a software source, and to upgrade from the last version of Ubuntu, which are useful for people who can get a cd in the mail more easily than downloading 100's of MB of data.