According to Interesting Thing of the Day, throughout European history rulers and power-seekers had a tendency to depose of their political rivals, spouses, and annoying neighbors by slipping a mickey into their vino -- a mickey that would kill them. Thus, it became customary for a host to pour wine from a single decanter and take the first sip, ensuring that it wasn't poisoned. From that custom comes the notion of "drinking to one's health."
Somewhere along the way, the custom of clinking glasses together developed for similar reasons. However, it wasn't a polite little "clink," it was more of a head on collision in which some of the contents of each glass would spill into the other -- again showing that neither was poisoned.
Now, to explain where the bread fits in, we've got to go back to ancient Rome where the quality of wine wasn't very consistent and the tendency to poison it was still relatively common. One day, someone had the bright idea to put a piece of severely burnt toast into their glass, using the carbon to remove unwanted flavors like a charcoal filter. Perhaps this also made it easier to smell hemlock in your cabernet, but I'm just guessing there.
Anyhow, this tradition eventually migrated all the way to England, where the word "toast" eventually began to refer to the wine, the glass, the whole "to your health" thing ... pretty much everything to do with drinking wine, regardless of whether giving a toast was actually involved or not.