First of all, let's go ahead and define a Mashup (this is from Wikipedia...)
A mashup is a website or web application that seamlessly combines content
frommore than one source into an integrated experience. Content used inmashups
are typically sourced from a third party via a public interface orAPI.
Many people are experimenting with mashups using eBay, Amazon,Google, and Yahoos APIs.OK, so a mashup is someone taking other people's content/applications and bringing them into their own website. In come cases, the mashup is better than the original content, because it provides additional context, or an interesting way to use the content/application.
There are lots of interesting Map mashsup (google, yahoo, mapquest, etc.) - some have taken a map and mashed it with a blog - allowing someone to do a "writeup" of my commute to work. Mashups are interesting - and it's cool that companies have figured out that someone else just might have a cool "alternative" use for their stuff -- something they would never have thought about. But, just like everything else, not all mashups are worth it - but you have to judge for yourself.
Mashups provide a great business opportunity, so get your juices flowing and check out some of these sites....
The Programmable Web - good directory, with description.
Mashup Camp web blogIvan Pope's API
Blog Mix'06 -- a gathering
And here are a few examples...
And you'll find more - google mashup, then do a blog search, technorati, tag it, whatever.