A natal chart (also called a birth chart) is a symbolic snapshot of the sky at the exact moment of your birth. In Western astrology it maps the positions of the Sun, Moon, planets, and major mathematical points across the 12 zodiac signs and 12 houses.
Short answer
A natal chart (also called a birth chart) is a symbolic snapshot of the sky at the exact moment of your birth. In Western astrology it maps the positions of the Sun, Moon, planets, and major mathematical points across the 12 zodiac signs and 12 houses.
In depth
Calculating a natal chart requires three pieces of birth data: date, time (ideally to the minute), and location. The location matters because the houses — the 12 sectors that map life areas — are calculated from the rotation of the Earth at your specific latitude and longitude.
The natal chart has multiple layers. The signs describe the qualitative tone of energy (Aries pioneering, Cancer nurturing, etc.). The houses describe the life domain (1st house = self, 7th house = partnerships, 10th house = career). The planets are the actors playing roles in those houses. The aspects (geometric angles between planets) describe how the actors interact.
Beyond Western astrology, the term "natal chart" is also used for Vedic sidereal charts, Chinese Ba Zi pillars, and Human Design BodyGraphs — all of which compute different symbolic structures from the same birth data.