An ordinary (tropical) birth chart uses the spring equinox — the start of Aries — as its zero point. A draconic chart takes the same planetary positions and uses the Moon's North Node as zero instead: an entirely different frame of reference.
The lunar nodes are the two points where the Moon's orbit crosses the apparent path of the Sun (the ecliptic). In both traditional and modern astrology the North Node is generally read as the direction being moved towards, not yet familiar, and the South Node as the tendency brought along, already well practised. The pair is often called the karmic axis.
A draconic chart takes the degree of the North Node in the birth chart and repositions every planet relative to that point — everything is shifted as though the North Node sat at 0° Aries. The result is a chart with exactly the same aspects (the relationships between planets do not change) but completely different sign and degree positions.
The draconic chart is one of astrology's less standardised but more intriguing techniques. Some astrologers interpret it as "the soul's deeper intention, from before birth" — a layer beneath the personality layer of the tropical chart. Its most common use is in synastry: the aspects between two people's draconic Suns or Moons are examined in search of a bond at a "soul level".
This technique is not part of the mainstream of traditional Western astrology; it is seen more often in modern, more spiritually oriented astrological circles.
The tropical foundation a draconic chart is derived from.
Another technique working from a different logic of time and reference.