What is a horizontal band saw?

It's a band saw where the blade is horizontal, not vertical like most band saws have it. These are fairly specialized tools.

There are two different kinds of these.

The first is the metal-cutting horizontal band saw. The saw is attached to a stand by a pivot, so you can cut with it like you would a chopsaw. These are used when cutting nonsparking metals (basically anything except ferrous metals), which shouldn't be cut with an abrasive wheel because the metal dust will clog the wheel, or when you're cutting in an environment where sparks would be dangerous.

The second is the wood-cutting horizontal band saw. These are also called portable sawmills. You use them when you're cutting boards out of a log.