The Omnibus is a two-decked open-air bus, its design inspired by early 20th-century motorized vehicles. It takes you on a 6-minute, "grand circle tour" of Tokyo Disneyland's Plaza. When they say "circle" they mean that literally; the trip is a 360-degree, clockwise ride around the Plaza.
You might be wondering why the Omnibus doesn't drive down Main Street like the vehicles at Disneyland in California do. There are several reasons for this: Tokyo Disneyland's Main Street (inside World Bazaar) is almost always jammed with people, regardless of the time of day. Disneyland's Main Street has a small plaza at the end of it; Tokyo Disneyland's does not, meaning the vehicles would have no place to turn around. Also, World Bazaar is covered, and although it's well ventilated, running these internal-combustion vehicles through it all day might lead to a bit of carbon monoxide in the air.
As the route the Omnibus drives covers some of the same ground that parades do, the Omnibus does not run at or around parade times. In fact, the schedule is so limited you may be lucky if you see it at all. During the trip the driver provides narration, but it is in Japanese only.
You can't really see anything from the Omnibus that you couldn't see from walking the same route, although the top level does provide a nice perspective. If you are going to ride the Omnibus, make certain that you sit on the left side (facing forward), and preferably on the top level.