The horizontal section of a bicycle frame that extends from seatpost to fork. It is possibly the most important section of the frame with regard to handling - a stiffer top tube makes the bike more responsive.
Women's bikes, up until the mid-90s, had a top tube that connected halfway down the seatpost, this allowed the rider to wear a skirt while riding and be involved in some spectacular crashes when cornering too hard pulled the tube away from the seatpost.
Some new bicycles have a top tube that is set at a downward slope (toward the seatpost), similar to the women's bikes of ages past, the key difference being that where the tube hits the seatpost is also where the seatstays start, meaning the frame is effectively a traditional frame, tilted at an angle. This is known as a compact frame, and was popularised by Giant.