The Tree of Life - the sephirot
The Tree of Life has ten circles - these are called "sephirot" (singular: sephira). Each sephira represents a "divine emanation" according to the classical Qabalah; in effect, it represents a map of the qualities of God. In the Zohar, a book put together in 1280 by the Spanish Qabalist Moses de Leon (but purportedly derived from the mystical writings of a second century Qabalist, Rabbi Shimon bar Yochai), it is written:
"God is unified oneness... Down to the last link, everything is linked with everything else; so divine essence is below as well as above, in heaven and on earth."
This is summed up by the phrase "As above, so below" and is a general principle in the Universe. For example, astrology is based on the premise that large-scale events in the sky (alignments of planets) have an influence on the small scale (a person's life and personality). In the Qabalistic sense, the huge concept of the body and mind of God is reflected in the smaller-scale body and mind of each individual human. To the Qabalist, we are truly made "in God's image", and the Tree of Life is a map of us as much as it is a map of God.

The tree has:
The sephirot are numbered in the order of the "lightning flash" (see Tree of Life History for details), starting with the creative spark at Kether and culminating in Malkuth at the bottom of the central pillar. Note that the names of the sephirot are Hebrew words, and their transliteration to English varies according to which book you read - for instance, Malkuth is sometimes spelt Malcut, Geburah spelt Gevurah and so on.
This page simply gives a quick overview of each sephira - click on the sephira on the Site Map to get full details and correspondences.
Kether
This means "crown" and represents the initial creative spark, the edge of the knowable Universe. Beyond Kether lies the great unknown - the veils of negative existence, the No-Thingness of the absolute void. It corresponds to the crown chakra in Eastern philosophy, and the highest level of enlightenment that a human can attain while still alive. The other sephirot also correspond to planets - Kether corresponds to the whole Universe (although some Qabalists correspond it to Pluto).
Chockmah
"Wisdom". The creative spark of Kether is unstructured, and Chockmah begins to give it direction; it corresponds to "The Word" of God. It corresponds to the third eye chakra, and the zodiac (some Qabalists correspond it to Neptune).
Binah
"Understanding". The Word has been uttered, now it starts to be understood. Like Chockmah, it too corresponds to the third eye chakra, and to Saturn.
These three sephirot should really be considered together - they are called the "Supernal Triad" and represent the human soul. Traditionally, Chockmah represents the male force, Binah the female force and Kether the genderless Godhead. Christian Qabalists may correspond this to the Holy Trinity of the Father, the Son and the Holy Ghost.
The Supernal Triad is separated from the rest of the Tree of Life by The Abyss - a horizontal line across the tree. Below the Abyss lie the sephirot of our everyday world, where everything is duality; the left and right halves of the Tree become significant, as we shall see. Above the Abyss, everything works in harmony. There is a "hidden" sephira that lies on the Abyss itself, called "Daath", or "Knowledge". This represents the Tree of Knowledge of Good and Evil mentioned in the Bible (see also Tree of Life: Bible).
Chesed
"Mercy". Represents personal love and awareness, and the way that these emotions and attributes affect our relationship with our community at large. It corresponds to the heart chakra, and Jupiter.
Geburah
"Strength" or "Severity". Represents personal will and power, and the way that this affects our relationship with our community at large. It corresponds to the heart chakra (like Chesed), and Mars.
Chesed and Geburah need to be considered together - they represent opposite sides of the same coin. Everything in life is a balance between severity and mercy - whether we are "too soft" or "too hard" on ourselves and on others. They are Archetypes, or principles, and as the Supernal Triad represents our soul, Chesed and Geburah represent the way that our soul manifests in the real world.
Chesed is the first sephira below the Abyss on the right-hand pillar (which corresponds to the left-hand side of the body - imagine the Tree is a "person" facing you), which is called the "Pillar of Mercy". Geburah is at the top of the "Pillar of Severity".
Tiphareth
"Beauty". This represents the "real you". You have a body, you have feelings, you have thoughts. Tiphareth is the "you" that has all these things. Too often, we find ourselves bogged down in the lower sephirot (emotions, thoughts, and so on). When we try to live within Tiphareth instead, we feel truly "centred" and balanced. It corresponds to the heart chakra, and to the Sun. Tiphareth is really a connecting point between the "upper" and "lower" parts of our personality; the heart chakra is effectively a trinity of Chesed, Geburah and Tiphareth.
Netzach
"Victory". This represents your feelings and emotions, both positive and negative. When you are moved by the beauty of the scenery, or enjoying a work of art, or feeling depressed and crying - you are experiencing the attributes of Netzach. It corresponds to the solar plexus chakra, and to Venus.
Hod
"Splendour". This represents your thoughts and intellect. When you are doing a crossword puzzle, arguing a point with someone or worrying about whether someone hates you because of something you said - you are experiencing the attributes of Hod. It corresponds to the solar plexus chakra (like Netzach), and to Mercury.
Like Chesed and Geburah, Netzach and Hod can be seen as opposites. True, they work very well together, but they can also represent different tendencies - some people are cold, calculating and logical (Hod-based), and others are hot-headed and emotional (Netzach-based). Tiphareth lies not on the left or the right pillar, but in the middle - so getting a sense of balance between these extremes is useful.
Yesod
"Foundation". We've just considered thoughts (Hod) and feelings (Netzach). Any action that takes place in the real world starts off as an idea - a combination of feeling (wanting to do something) and thought (deciding to do it). Yesod is the sephira that puts this all together, and initiates its manifestation. It can be thought of as the "subconscious" and although it is often associated with sexuality, it is far more than this. It's the place where all those brilliant ideas that you never quite got round to doing spend their time! It corresponds to the sexual chakra, and the Moon.
Malkuth
"Kingdom". The physical realm, and your physical body and sensations. Running, eating and drinking, physical pain and exhaustion - these are all part of Malkuth. It's also where actions do manifest, if you let them. The lightning flash that created the Universe replays again and again within us every time we do something. You have a yearning in your soul to do something (Kether, Chockmah, Binah). This filters through to your awareness, and you have the will to do it (Geburah, and hopefully tempered by Chesed - weighing up the pros and cons, and considering what effects your actions would have). Then, you decide that you really do want to do it (Netzach) and work out how to (Hod). Then comes the final surge (Yesod) and you get on and do it, manifesting what you want in the real world (Malkuth). Malkuth corresponds to the base chakra, and to Earth.
This is just an overview of the sephirot. Each sephira has numerous associations with colours, plants, animals, angels, and a whole range of experiences associated with each one. Look at the individual links for more details, and some practical exercises, visualisations and meditations associated with them.
In addition to the sephirot, there are also 22 paths. Each path also has its own correspondence - in particular, each path corresponds to a Hebrew letter, and to a major arcana card of the Tarot, as well as to colours, plants and so on.