What it is
Navamsa divides each sign into nine equal parts of 3°20′. The 108 padas (quarters) of the 27 nakshatras are exactly this size, so every nakshatra pada corresponds to one navamsa. That is why navamsa is often called the companion of the main chart: astrologers look at D1 first, and D9 right after.
How it is calculated
Rule: in a movable sign (Aries, Cancer, Libra, Capricorn) the first part belongs to the sign itself; in a fixed sign (Taurus, Leo, Scorpio, Aquarius) to the 9th sign from it; in a dual sign (Gemini, Virgo, Sagittarius, Pisces) to the 5th from it; then onward in order. As a result every fire sign's navamsas start from Aries, earth signs' from Capricorn, air signs' from Libra and water signs' from Cancer.
Example: a planet is at Aries 17°. 17 ÷ 3°20′ = 5.1, so the sixth part. Aries is movable, so the sixth sign from Aries: Virgo. In D9 the planet is in Virgo. At Taurus 17° the count would start from Capricorn, the 9th from Taurus, and the sixth part would be Gemini.
ePandit's engine does the same thing with one line of arithmetic: multiply the planet's sidereal longitude by 9, wrap it into 360°, and the sign you land in is the navamsa. Aries 17° = 17°; 17 × 9 = 153°, which falls in Virgo. The two methods give the same answer every time.
What tradition looks at in it
Parāśara links the navamsa to the marriage partner. Tradition looks at the lord of the 7th house, Venus, and, in a woman's chart, Jupiter, as tradition has it. This gives a glimpse of how a person connects in partnership, what kind of companionship feels natural, and what they bring to a relationship.
Navamsa is also associated with dharma: 'nava' means nine, and the 9th house is the house of dharma and fortune. Tradition reads in it a glimpse of a person's values and direction in life.
The third theme is the inner strength of planets. Tradition holds that D1 shows a planet's outer form and D9 how easily that planet can do its work from within. That is why it is customary to check a planet's navamsa before speaking about its results.
Vargottama
When a planet is in the same sign in both D1 and D9, it is called vargottama. Every sign has one such navamsa: the first in a movable sign, the fifth in a fixed sign, and the last (ninth) in a dual sign. For instance, a planet between Aries 0° and 3°20′, or between Taurus 13°20′ and 16°40′, is vargottama. Tradition holds that a vargottama planet expresses its themes with steadiness and ease. It is taken as a good sign, but it decides nothing on its own.
How much the birth time matters
On average the ascendant moves about 1 degree every 4 minutes; some signs rise faster, some slower. One navamsa is 3°20′, so a difference of roughly 13 minutes in birth time can change the D9 ascendant, and less if the ascendant is near a boundary. The Moon crosses one navamsa in about 6 hours, and the other planets more slowly still. In your chart, ePandit shows next to every varga how many minutes of birth-time change would shift its ascendant. If your time is uncertain, lean on the planets' navamsas rather than the D9 ascendant.
How to read it calmly
Read the navamsa as a second look, not a verdict. Tradition first studies the 7th house and its lord in the main chart (D1), then the running dasha; the navamsa helps check whether the same theme shows up here as well. A planet's sign in D9 decides nothing on its own, and tradition does not label a planet's varga placement as a problem.
Relationships are built by two people's understanding, conversation and companionship. Navamsa is one traditional language for them, not a final judgement. To see your own navamsa, choose D9 in the free kundli.