Once again, Jim Mahar at Financeprofessor.com brings us some useful material for the classroom. He links to this piece by Don Chance in Financial Engineering News, titled "A Non-Technical Introduction to Brownian Motion". It's perfect for students who want a relatively low-tech explanation of brownian motion and weiner processes.
For those with better math chops, there's also Shimko's Finance in Continuous Time: A Primer. It's still fairly approachable (hey - it got me through grad school, so it can't be too hard.)