What Makes Up the Name: web + broadcast
Listen, in five years, broadcast and webcast will all be the same thing so enjoy this one while you still can. Webcast!
Origin: According to the always reliable* wikipedia, "Webcasting was first publicly described and presented by Brian Raila of GTE Laboratories at InterTainment '89, held in New York City, USA." So take that for what it's worth, but people didn't really start to stream content online until the mid to late 90s, and it wasn't really any good until the early 2000s.
*not always reliable
See Also: webisode, netcast, podcast