It was explained to me that the giant full moon of this last April 16th appeared so bright and large because the moon was the closest to the Earth that it ever has been or ever will be (within a thousands of years kind of span.) How is this possible?
The Moon's orbit around Earth isn't a perfect circle - it's actually fairly elliptical - about 5.5% eccentricity. This means there's a fairly large difference between the perigee (when the Moon is at the closest point in its orbit) and apogee (when the Moon is at its farthest). This means that the Earth-Moon distance varies by about 13,000 miles either direction of the average distance. So if the full moon occurs at or near perigee, it appears noticeably larger in the sky than if it occurs at apogee, and it also it is brighter, because the amount of light received by the Earth from the Moon depends not only upon the amount of light the Moon gives off, but also how far the Earth is from the Moon. The farther the Moon, the smaller the fraction of the Moon's light that reaches Earth. I should add, however, that while this is a significant effect, all full moons are large and bright, so it's difficult to tell the difference without being able to look at a perigee and apogee full moon side by side. This year, the lunar perigee occurred only hours from the full moon on April 16th. It was the closest full moon of the year, but not the closest the Moon has been to the Earth in recent times. The nearest perigee recently was in 1912. For a much more detailed explanation, check out this site - it even has a link to a perigee and apogee calculator so if you want to observe this phenomenon you'll know when to take a look!
What other factors affect the brightness of the full moon?
There are several other factors that affect the brightness of the full moon. When the Earth (and therefore the Moon) is at its perihelion, the closest point in its orbit to the Sun, the sunlight that reflects off the Moon is slightly more intense, causing the full moon's brightness to increase by about 4%, which is imperceptible by the human eye.
The brightness of any object, including the moon, in the sky increases with its height in the sky. When an object is directly overhead, its light strikes the ground at a right angle, and the intensity of light is the same as the intensity in the beam. However, when an object is nearer to the horizon, its light strikes the ground at an angle, and the same amount of light is spread out over a larger area. Therefore, less light per unit area reaches the ground from an object near the horizon. Also, the closer the moon is to the horizon, the more atmosphere the light must travel through to reach the observer. This means that more of the moon's light is absorbed or scattered by the atmosphere. The height of the moon in the sky results from a combination of the latitude you are observing from and the declination of the moon.
When the moon is closer to opposition, that is, the point exactly opposite the Sun (at which point there is a lunar eclipse because the Sun's light is blocked by the Earth and does not reach the Moon), it is brighter. This is called the opposition effect. It is believed to be caused mainly by shadow hiding. The closer the moon is to opposition, the smaller the shadows cast by objects on its surface, and the brighter it appears. For more information on the opposition effect, check out this website.
Finally, atmospheric conditions have a great effect on the brightness of the full moon. The full moon on a clear night will be much brighter than if there is a lot of dust, smog or clouds.
Happy Full Moon watching!