Barber hones are usually small, hand-held synthetic hones which are suitable for maintaining a straight razor's shaving edge. They are usually very hard, so they tend to wear very slowly can take a long time to lap. Some claim barber hones do not require lapping, and certainly many barbers have used such hones for great lengths of time without lapping them. Some barber hones are dual grit, with a finishing side and a coarser side. The exact grits of barber hones are unknown, but the finishing surfaces of barber hones are commonly thought to be around the 6k to 10k grit range.
Barber hones tend to be fast cutters, generally requiring less than 10 honing strokes to refresh the edge of a razor that is just beginning to pull. If the edge is still not sharp enough after 10 strokes, a second or third set of 10 strokes may be needed. As long as a razor's edge remains undamaged, its shaving edge can be maintained with a barber hone indefinitely. This would have been ideal for a barber, who would have to keep his razors as keen as possible between shaves. For ease of use, barber hones were designed to be used with water, lather, or dry. Not waiting until the razor edge is too far gone seems to be the trick with barber-hones.
Here are links to discussions on barber hones and their use.
Examples of barber hones:
Franz Swaty 3-line hone
Franc Swaty (Francis Swaty) Maribor Jugoslavija 3-line hone
Franz Swaty Marburg Austria 2-line hone
Frictionite 00 barber hone, with a slurry stone included.
This is a GRACO strop/hone by the Henry Graves Razor Company. A cut of leather is attached to the backside of the hone for stropping.
This is an example of a Swastika brand hone.