The Ascendant is the zodiac sign that was rising on the Eastern horizon at the moment the chart is calculated for (like a Natal chart). If someone is born around sunrise, the Sun will be found close to the Ascendant in their chart. In most house systems, it is the cusp of the 1st House in the chart. It is one of the four angles in the chart.
In natal astrology, the Ascendant sign and 1st house show how you come across to other people (as opposed to how you see yourself inside, which is more reflective of the Sun or sometimes the Moon). The Ascendant sign may also indicate certain physical characteristics, including face shape and features.
The Ascendant (sometimes called the Rising Sign) is always opposite the Descendant in the chart. Some modern astrologers associate the Ascendant and 1st house with the zodiac sign Aries.