Wood stain is different from paint in that, rather than completely covering the wood with a new color and texture, it lays down a pigment over the wood fiber that will deepen or change the natural color of the wood while still preserving the grain and texture. Stain does not actually bond itself to the wood fibers, but instead relies heavily on pigment and bonding agents to create a finish over the top of the wood.
Varnish is quite different from stain in that it is not intended to add pigment or coloring to the wood, but rather to create a transparent, glossy finish that also acts as a sealant to protect the wood from the elements. Varnish is especially useful on wood pieces that see a lot of use, as it will provide an easily cleanable surface and will help prevent scratches or stains.
Shellac is similar to varnish in that it creates a hard, semi-glossy finishing seal over the wood to which it is applied. But it is dissimilar to varnish because, while varnish is primarily made from a combination of oils and thinners, shellac is made from the processed secretions of the Indian Lac bug. Shellac also acts as a coloring finish and is extremely effective at sealing wood surfaces against moisture.
Polyurethane is a fast-drying finish that creates a hardened protective coat and moisture seal over the wood to which it is applied. Polyurethane is typically a clear, high-gloss finish but can also be purchased in a variety of colors if you prefer non-clear finishes. Several coats of polyurethane may be needed to achieve an effective finish, depending on the brand and the type of wood.
Since mantles are almost always located immediately above a rather large heat source—the fireplace—it behooves you to select a finish that is more heat resistant than others, depending on how much the fireplace gets used. Reactant finishes, such as varnish or linseed oil, are far more heat-resistant than evaporative finishes like polyurethane or shellac.