Eclipses occur when the Moon and Earth are aligned so precisely that one passes through the other's shadow (cast by the Sun). There are two kinds of eclipses: Solar Eclipse and Lunar Eclipse. Each type typically happens twice a year.
A Solar Eclipse is a supercharged New Moon, and a Lunar Eclipse is a supercharged Full Moon, made more powerful because of their precise alignment. Most of the time, eclipses happen in pairs – one solar and one lunar or vice versa. The two weeks in between eclipses often feel very intense – like two weeks of Full Moon energy!
We get a set of eclipses about every 5½ months. So, there are typically 2 sets of eclipses every year (sometimes sort of 2½ if a set from the previous or following year overlaps at the turn of the year), sometimes referred to as "eclipse seasons."
Each eclipse is visible from a different location around the world, so you might not be able to see it where you live. However, even if the eclipse is not visible where you are, the astrological influence is still there. Be sure catch a glimpse of the Moon at night around eclipse season, since it is especially bright in the sky in the two weeks before and after the eclipses.
Occasionally there is an extra eclipse, so that there are 3 eclipses in a row instead of the usual 2 – lunar-solar-lunar or solar-lunar-solar. This happens about 12% of the time, on average. An even rarer occurrence is when both sets of eclipses in the same year are triple eclipses, which happens only about 3% of the time! The last time it happened was 1951 and it won't happen again until 2096.
WARNING: You must never watch a solar eclipse without proper eye protection or you can damage your eyes, often permanently. Find out more about the astronomy of eclipses. On the other hand, it's completely okay to look directly at a lunar eclipse. How can you tell if it's a solar or lunar eclipse? Easy! Assuming it's visible from your geographical location: if it's nighttime, it's a lunar eclipse. If it's daytime, it's almost certainly a solar eclipse.
How long does an eclipse's energy last? Well, it depends... More about that in the Timerange article.
See also: Eclipse times.