The Ascendant (also known the "rising sign") is the sign on the cusp of the first house of the natal chart. It is the sign (and degree of that sign) that is rising on the Eastern horizon at the moment of birth, with respect to the place of birth.
The Ascendant is one of the four angles of the chart. The other three are the Descendant (directly opposite the Ascendant), the Imum Coeli (IC), and the Midheaven (MC).
The Ascendant defines, in part, the first impression we make on others in a personal rather than professional sense. It represents our physical appearance, our physical bodies and overall health, and the body ego. The Ascendant is often referred to as the mask we wear, although I don't consider it to be as superficial as this might suggest. What it does represent is our natural and personal defence mechanisms that we use to adapt to, and cope with, our environment.
The Ascendant also shows our first impressions of the world around us, and reveals our expectations of the world around us--whether we are naturally hesitant or enthusiastic, for example. How we begin new projects, and our attitude towards new experiences come under the rule of the Ascendant.