The ascendant is the zodiac sign that was rising on the eastern horizon at the moment you were born. Unlike your Sun sign (one for the whole day), the ascendant changes roughly every two hours — so people born on the same day, just at a different time or in a different city, end up with a different ascendant.
That's exactly why precision matters so much for the ascendant: you need a birth date, a birth time accurate to at least a few minutes, and a birth city — actual coordinates and time zone, not just a country name. A 4-minute difference in time shifts the ascendant by almost a degree — enough, right on the border between two signs, to land you in a different one entirely. If the time is completely unknown, the ascendant is honestly unavailable: guessing from an approximate time means passing off one sign as another.
The ascendant is a common reason behind "you don't seem like your sign at all": if an Aries with a straightforward Sun has an ascendant in Pisces, the first impression will read softer and more yielding than the Sun sign alone would suggest — the underlying character hasn't gone anywhere, it's just not on the surface.
The ascendant sets up the system of twelve houses — the first house is counted from it, and the rest follow around the circle. That's why it's sometimes called a "mask" or a "first impression": not the whole character (the Sun and the rest of the chart cover that), but how a person comes across outwardly — first reaction, behavior in a new setting — often noticeable before you actually get to know someone.
The ascendant is part of the natal chart — it isn't calculated separately here: build your chart with a birth time and place, and you'll see your ascendant alongside the rest of the reading.