Sweetbreads are the two portions of the thymus gland (one in the throat and one in the chest cavity) of young animals. The rounder, fatter sweetbread from the heart is usually considered the better of the two.

Sweetbreads may be fried gently in butter until brown or braised slowly.
Calf's Sweetbreads
These are considered the finest type of sweetbread, especially the large ones from milk-fed veal. They have a delicate flavour and are much less fiddly to prepare than lamb's sweetbreads. However, they are in short supply and tend to be relatively expensive.
Lamb's Sweetbreads
Although smaller than calf's sweetbreads, they are still tasty and are considerably cheaper to buy.