Because this is a well-known subject, I will just quote from Wikipedia. I've included a few notes in each case. Although in astrology the Zodiac signs and the planets are distinct, they clearly embody the same psychological or psycho-social archetypes. Thus there is a sort of redundancy in modern astrology.
From the Wikipedia page "Astrology"
The zodiac is the girdle or band of constellations through which the Sun, Moon, and planets transit across the sky. Astrologers noted these constellations and so attached a particular significance to them. Over time they developed the system of twelve signs of the zodiac (Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces), based on twelve of the constellations they considered to be particularly important. The Western and Vedic zodiac signs have a common origin in the tradition of horoscopic astrology, and so are very similar in meaning. In China on the other hand, the development of the zodiac was different. Although the Chinese too have a system of twelve signs (named after animals), the Chinese zodiac refers to a pure calendrical cycle, as there are no equivalent constellations linked to it like the Western or Indian zodiacs. The common choice of twelve zodiac signs is understandable considering the interaction of the Sun and Moon was central to all forms of astrology.
The majority of Western astrologers base their work on the tropical zodiac which divides the sky into twelve equal segments of 30 degrees each, beginning with the first point of Aries, the point where the line of the Earth's celestial equator and the ecliptic (the Sun's path through the sky) meet at the northern hemisphere spring equinox. Due to the precession of the equinoxes, the slow changing of the way Earth rotates in space, the zodiacal signs in this system bear no relation to the constellations of the same name but stay aligned to the months and seasons.
Practitioners of the Vedic astrological tradition and a minority of Western astrologers use the sidereal zodiac. This zodiac uses the same evenly divided ecliptic but approximately stays aligned to the positions of the observable constellations with the same name as the zodiacal signs. The sidereal zodiac differs from the tropical zodiac by an offset called the ayanamsa, which steadily increases as the equinoxes drift further. Furthermore, some siderealists (i.e. astrologers employing sidereal techniques) use the actual, unequal constellations of the zodiac in their work.
From the Wikipedia page "Astrological sign" (with comments added; also, some paragraphs edited or deleted)
The twelve signs
In Western astrology the zodiac of twelve sign represents twelve types of personality. The zodiac traditionally begins with Aries. The following are the twelve zodiac signs in order.
- Aries (The Ram) (cardinal, fire, personal): In astrology Aries is ruled by the planet Mars. The tropical duration of Aries is March 21 to April 20.
- Taurus (The Bull) (fixed, earth, personal): In astrology Taurus is ruled by the planet Venus and for a few modern astrologers, the dwarf planet Ceres. The tropical duration of Taurus is April 21 to May 20.
- Gemini (The Twins) (mutable, air, personal): In astrology Gemini is ruled by the planet Mercury. The tropical duration of Gemini is May 21 to June 21.
- Cancer (The Crab) (cardinal, water, personal): In astrology Cancer is ruled by the Moon. The tropical duration of Cancer is June 22 to July 22.
- Leo (The Lion) (fixed, fire, social): In astrology Leo is ruled by the Sun. The tropical duration of Leo is July 23 to August 22.
- Virgo (The Virgin) (mutable, earth, social): In astrology Virgo is ruled by Mercury. The tropical duration of Virgo is August 23 to September 22.
- Libra (The Scales) (cardinal, air, social): In astrology Libra is ruled by the planet Venus. The tropical duration of Libra is September 23 to October 22.
- Scorpio (The Scorpion) (fixed, water, social): In astrology Scorpio is ruled by the planet Pluto. The tropical duration of Scorpio is October 23 to November 22.
- Sagittarius (The Archer) (mutable, fire, universal): In astrology Sagittarius is ruled by the planet Jupiter. The tropical duration of Sagittarius is November 23 to December 22.
- Capricorn (The Sea-goat) (cardinal, earth, universal): In astrology Capricorn is ruled by the planet Saturn. The tropical duration of Capricorn is December 23 to January 19.
- Aquarius (The Water Carrier) (fixed, air, universal): In astrology Aquarius is ruled by the planets Saturn and Uranus. The tropical duration of Aquarius is January 20 to February 19.
- Pisces (The Fish) (mutable, water, universal): In astrology Pisces is ruled by the planets Jupiter and Neptune. The tropical duration of Pisces is February 20 to March 20.
The Zodiac Signs and the elements (I can't recall where I found this graphic)
The four elements
Each sign is associated one of the classical elements (water, fire, earth and air.)  Fire and Air signs are positive or extrovert, masculine signs; while Water and Earth signs are negative, introvert, feminine signs.
- Fire Signs--Aries, Leo, and Sagittarius-- Fire represents one's desires and creative energies.
- Earth Signs--Taurus, Virgo, and Capricorn-- Earth represents one's material resources, environment and possessions.
- Air Signs--Gemini, Libra, and Aquarius-- Air represents the intellect and one's ability to reason and communicate.
- Water Signs--Cancer, Scorpio, and Pisces-- Water represents imagination, human feelings and one's ability to love and sustain.
The Three Qualities
The Qualities assign the Signs into Quadruplicities, three groups of four.  They are occasionally referred to as crosses because each quality forms a cross when drawn across the zodiac. Christian astrology relates the three qualities to the three aspects of God in the trinity.
- Cardinal signs (Aries, Cancer, Libra and Capricorn) are associated with initiation and creativity.
- Fixed signs (Taurus, Leo, Scorpio and Aquarius) are associated with stabilization and determination.
- Mutable signs (Gemini, Virgo, Sagittarius and Pisces) are associated with resourcefulness, holism and adaptability.