A satellite is said to rotate synchronously if the period of its rotation about its axis is the same as the period of its orbit around its primary. This implies that the satellite always keeps the same hemisphere facing its primary (e.g. the Moon). It also implies that one hemisphere (the leading hemisphere) always faces in the direction of the satellite's motion while the other (trailing) one always faces backward. Most of the satellites in the solar system rotate synchronously.
Astronomer Giovanni Schiaparelli had thought that the planet Mercury rotates synchronously around the Sun, but in the early 1960s astronomers found out it rotates faster than that. It makes 3 rotations for every two revolutions.