Layer 1 — the houses
The chart is split into twelve houses (bhavas) starting from the ascendant. The 1st house is you and your body, the 2nd is money and family, the 7th is partnership, the 10th is career and public life. A planet's result depends a lot on which house it sits in from your lagna.
Layer 2 — the nine planets
Vedic astrology uses nine grahas: Sun (soul), Moon (mind), Mars (drive), Mercury (speech and logic), Jupiter (wisdom and luck), Venus (love and comfort), Saturn (discipline and delay), plus Rahu and Ketu — the karmic axis. Each planet is a verb; the house tells you where it acts.
Layer 3 — signs and nakshatras
The sign a planet sits in changes its tone — Mars in Aries is a sword, Mars in Pisces a scalpel. Finer still, each planet sits in one of 27 nakshatras (birth stars), which add flavor and drive the dasha order. The Free Kundli tool labels all three layers for every planet automatically.