Just like the name implies, half-round gutters look like you took a fully-enclosed pipe and cut it in half lengthwise. Half round systems offer a more historical and elegant look than the standard gutters. They are arched so that they collect rain or melting ice and then divert it to the downspout.
Because of their classic style, they are often used on older homes that are restored or on new construction that is intended to have a classic look. Historically half round systems were primarily applied to upscale homes. However, the emergence of half round systems has opened the market for half round to be installed on more modest homes.
Not only are they preferred for their aesthetic quality, but they are considered a superior type of system.