The “ascendant” (or “rising sign” — these terms are used interchangeably) refers to the sign that is “rising” or on the Eastern horizon at the time of birth.
It sets up the rest of the astrological house structure — the 12 sectors that correlate to important life areas — and determine where the planets and other points fall in a natal chart.
This is why knowing the exact moment of birth is so important to astrologers. Most predictive work relies more heavily on houses (which are again determined by the birth time and thus the ascendant) than most lay people realize.
Even weekly horoscopes and monthly forecasts are written more from the perspective of the rising sign than the Sun sign.