Lunar occultations happen when the moon passes in front of a star, major planet or minor planet. Grazes happen when a star passes behind hills and valleys close to the moon's north or south pole. When this happens the star seems to wink on and off several times. The 'graze zones' are a mile or two from the edge of the lunar occultation path. Amateurs can observe and time lunar occultations to help astronomers refine their knowledge of the lunar topography and help map the lunar limb profile as well as helping with lunar orbit dynamics and stellar positions.
Planetary occultations happen when a planet or asteroid passes in front of a star.
Amateurs can observe and time asteroidal occultations to help astronomers determine the size and shape of the asteroid. Jovian satellite eclipses are when one of Jupiter's moons blocks the sunlight onto another or passes in front of another. Observing and timing these events provides information of the satellite's position with respect to Jupiter. This has helped NASA plan exploratory spacecraft missions. This is a relatively easy task for amateurs to do.