A solder sucker is a device which is used to remove solder from a printed circuit board (PCB), as opposed to a desoldering bulb or solder wick. It is usually a small, spring-loaded device that "sucks", as the name implies, the solder off the previously soldered connection. The way one typically works is, it's first applied to a heated solder connection, then the user activates the device (usually via button) to "suck" the solder away. Other models use a motor powered vacuum pump instead of spring to generate the vacuum.
However, solder suckers that rely on sudden, fast flow of air could damage the fragile SMT components. Hence, high-end solder sucker uses a vacuum pump that gives constant airflow, which is much less damaging than the sudden vacuum of air from a spring-loaded solder sucker.