What is the Atmakaraka?
Atma means soul and karaka means significator. In the Jaimini system the planets are ranked by the degree they have reached within their own sign, ignoring which sign that is. The planet with the highest degree is the Atmakaraka, the next is the Amatyakaraka (career and counsel), and so on down to the Darakaraka, the planet with the lowest degree, which signifies the spouse.
These are called chara karakas, meaning movable significators, because unlike the fixed karakas (the Sun for the father, Venus for marriage) they are different in every chart.
The 7-karaka and 8-karaka schemes
Two schemes are in use. The seven-karaka scheme ranks the Sun through Saturn and leaves out Rahu and Ketu. The eight-karaka scheme adds Rahu, ranked by 30 degrees minus its degree because it moves backwards through the zodiac. Ketu is not a chara karaka in either scheme.
The two schemes agree about the Atmakaraka in most charts, but not always, and they disagree about the Darakaraka more often. Choose the scheme your tradition uses; the eight-karaka scheme is the default here.
How to read your Atmakaraka
Start with the planet itself, since each carries a different theme, then its sign and the house it occupies counted from the Lagna. The navamsa sign of the Atmakaraka is called the Karakamsha, and Jaimini astrologers read the whole chart from it as a second lagna. You can cast the navamsa with the D9 calculator linked below.
The meanings shown with your result are the traditional general readings. They describe a theme to look for, not a prediction, and are best read together with the rest of the chart.