Click on the thumbnails to see the screenshot.

The desktop and about dialog.

The most noticeable difference between 10.3 and previous versions is the brushed metal look windows get. Quicktime has had this for a while.
There is also a new sidebar for displaying icons and links.

Clicking the elliptical button in the upper right will display the window in "classic mode".

Note that the pinstripe background is no longer the background of the dock, and that it has been subtly dimmed down elsewhere.

A notable addition to Mac OS 10.3 is Exposé (with an accented "e" at the end).
Expose allows you to easily view which windows are open, and bring one to the front. It can be activated either by a specified keyboard key, or by moving the mouse into a specific corner.

Most importantly, no more Internet Exploder! That alone is a significant improvement.
Safari is now the default and standard web browser of Mac OS. It is based upon Konqueror.