What is the Ascendant (Lagna)?
The Ascendant is the point of the ecliptic crossing the eastern horizon at birth. Ascendant, Lagna and rising sign are three names for the same thing. Its sign becomes the first house, and the sign after it the second, and so on around the chart.
Because the houses are counted from the Lagna, it decides which planet rules each part of life in your chart. The same Jupiter in the same sign means something different for a Cancer Lagna than for a Capricorn Lagna, since it rules different houses in each.
Why the exact birth time and place both matter
The Earth turns 360 degrees in a day, so the Ascendant sweeps the whole zodiac in about 24 hours: roughly one degree every four minutes. A sign is 30 degrees, so the rising sign changes about every two hours. Some signs rise faster than others, and the pace also depends on the latitude of the birthplace, so it can be anywhere from one to three hours.
That is why a birth time that is off by even 15 or 20 minutes can move the Ascendant several degrees, and near a sign boundary it can change the sign itself. Birth place matters for the same reason: the horizon is different at different latitudes and longitudes.
Ascendant, Moon sign and Sun sign compared
Your Sun sign is what popular horoscopes use and changes about once a month. Your Moon sign changes about every two days. Your Ascendant changes about every two hours, which is why it is the most individual of the three, and why two people born on the same day can have very different charts.
What the Ascendant tells you
Vedic astrology reads the Lagna as the self: body, constitution and the general direction of the life. Its ruling planet, the Lagna lord, is the most important planet in the chart, and the Lagna also determines which planets are yogakarakas and which gemstones suit you.