The planetary ruler of your Sun sign is important, and its myths and attributes tell you a lot about your own nature. For example, if your Sun is Sagittarius, your planetary ruler is Jupiter. You radiate in an expansive, faithful way, just as Jupiter acts as a cosmic guide to life's lucky breaks. And the house in which your Sun sign falls, is the life area in which you expand. The planetary ruler of your Sun's house position is like the host, who directs that Jupiter-ruled quest toward a particular life theme or lesson.
Each planet is a symbolic ruler of one (or two) Zodiac signs, and this helps you understand another dimension of that sign. The planetary ruler goes along with the sign and house, when you're trying to intuit the essence of a planet's position in your chart. These associations were grandly thought out during astrology's hay day in Greece, and came from observations of human behavior.
Once you know astrology, the links are clearer. Each planets has its own attributes, and are even dropped into daily language – mercurial, venusian, jovial, saturnine, etc. The pairings were originally made with just the planets in view, with Saturn at the outer edge. When new planets were discovered, astrologers altered these rulerships, based on what was observed. A new addition has been Chiron, a comet discovered in 1977, that's since been linked to Virgo, though most still list Mercury as the ruler.
There's a planetary ruler of both signs and houses, and this kind of intuitive synthesis is a key to “getting” astrology. Planets in their own signs, like Moon in Cancer, are said to be dignified, and that's a placement of strength. And yet, that Cancer Moon may sit in the Second House, the natural house of Taurus, ruled by Venus. This tells us that the Cancer Moon will seek to nurture via the senses, and likely be a great gourmand!
The Sun rules Leo.
The Moon rules Cancer. Mercury rules Gemini and Virgo (recently also associated with Chiron).
Venus rules Taurus and Libra.
Mars rules Aries (and Scorpio).
Jupiter rules Sagittarius.
Saturn rules Capricorn.
Uranus rules Aquarius.
Neptune rules Pisces.
Pluto rules Scorpio.