From "The Great Food Almanac" by Irena Chalmers:
Q: Why is a speech proposing someone's health called a toast?
A: Because in 17th century England it was customary to float a piece of spiced toasted bread in a bowl or carafe of wine to improve its flavor before it was drunk. When people raised their glasses in the traditional custom of drinking to wish someone good health, it would have been rude, as well as unwise, not to finish every drop, and so the toast was consumed along with the wine.
Chalmers notes that although the toast was eventually jettisoned (probably because the quality of wine became more consistently good), the term of making "a toast" survived.