What do degrees mean in astrology?

The astrological chart is a geocentric picture of the heavens for a given moment in time. The Earth is the circle at the center of the chart. The space around the Earth is represented by a circle of 360° encompassing the zodiac. The Earth is considered stationary and the zodiac "rotates" about the earth. Each section of the sky is then cut into 30° slices about the earth and these are called the houses. The degrees that a planet or house cusp occupies represent a piece of the sky in which that planet or hypothetical point were found in the sky at that given point in time.

Degrees arguably have special significance to some astrologers and not to others.

The Cusp and Critical Degrees:

In general the very first and last degrees are considered significant. They often carry the traits of the proceeding (0°-5°) or following (26° - 29°) sign. This is known as "being on the cusp". They are also called Anaretic degrees and one can expect to learn many lessons through the planet in that degree range.

The Decans: Each zodiac sign is comprised of 30°. Those signs are further cut into 10° segments called decans. Those born under a certain decan are said to also possess characteristics of the planet that decan.