Most modern telescopes are reflectors, with the primary element being a very large mirror. Historically, a fixed weight-to-diameter relation was used to build these mirrors, limiting their maximum diameter to 5 or 6 meters (200 or 230 inches), like in the Palomar Observatory.
A new generation of telescopes uses instead very thin mirrors, which are too thin to keep themselves rigidly in the correct shape. Instead, an array of actuators behind the mirror keeps it in an optimal shape.
The combination of actuators, a quality-of-image detector, and a real-time computer program to move the actuators to obtain the best possible image is termed active optics.
The "activeness" in their name means that the system keeps the primary mirror in its optimal shape against all environmental factors such as gravity (at different telescope inclinations), wind, telescope axis deformation, etc. Active optics correct all factors that may affect image quality at timescales of one second or more.
Active optics should not be confused with adaptive optics, which operates on a much shorter timescale to compensate for atmospheric effects, rather than for mirror distortion. Factors that affect the image at faster timescales (1/100th seconds or even less) are usually caused by the atmosphere and are not easily corrected with primary mirrors. For these, the adaptive optics technology has been developed for use with small corrective mirrors and recently for secondary mirrors.