What planetary hours are
Daylight is divided into 12 equal parts and the night into 12 more. Those hours are almost never 60 minutes long: in June in London a daytime hour runs about 82 minutes while a night hour is about 38. The closer to the pole and to the solstice, the wider the gap. That is why the boundaries are counted from actual sunrise and sunset rather than from midnight.
The Chaldean order
The hours are ruled by the seven visible lights in order of decreasing apparent speed: Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon. The sequence loops, so the Moon is followed by Saturn again. Taken every 24 hours, the same sequence produces the familiar order of the weekdays.
The day ruler and the first hour
The first hour after sunrise belongs to the planet the day is named after: Monday to the Moon, Tuesday to Mars, Wednesday to Mercury, Thursday to Jupiter, Friday to Venus, Saturday to Saturn, Sunday to the Sun. The rest follow the Chaldean loop. The astrological day starts at sunrise, so before dawn the previous day is still running.
What they are used for
Planetary hours belong to electional astrology, where the timing of an action is chosen deliberately: money talks are often set in an hour of Jupiter or Venus, a decisive move in an hour of Mars, paperwork in an hour of Mercury. This is not a forecast but a way to match the timing to the nature of the task.