At a basic level a meteor shower is a greater than average number of meteors occurring over a couple of nights, all originating from the same location in the sky. In fact, this is how meteor showers are named. The Perseids are called the Perseids because the meteors appear to all come from the same location in sky, in this case the constellation of Perseus. Meteors are bits of debris, often material the size of a grain of sand, that burn up as they fall through Earth's atmosphere. Very few meteors ever make it to the surface of the Earth before burning up. As they burn up, they appear as a streak of light across the sky that is commonly referred to as a falling star. Of course, no star is falling. It's just small debris falling through Earth's atmosphere.
Meteor showers are the result of Earth passing through comet tails. Comets leave behind a tail of particles that remain in an orbit. Each year, as Earth passes through this tail of particles, many enter Earth's atmosphere. Because Earth enters the tail in a specific direction, all of the meteors appear to originate from the same location in the sky.
The Perseids are a result of Earth passing through the tail of Comet Swift-Tuttle. There you go. Now you know the basics of meteor showers. Now you can head out later this month to observe the Perseids.