No matter where you are in a room, you can hear sound that emanates from a single hole. You can see light that spills through a small crack. You are picking up on waves, even though they're getting through spaces that aren't anywhere near you. Christian Huygens figured out why.
If you've seen a wave roll in along a beach, or over the length of an aquarium, or even along your bathtub, you've probably seen Huygens' principle in action. When the wave comes to a barrier that has one opening, the wave comes through the opening. It doesn't come through in the same shape as it went in, though. When the long plane of a wave comes through the opening, it "bends" around the corners of the opening, and continues moving outwards in a rainbow-like arc.
This arc is one of the reasons you can hear sound in another room, as if the sound were bending around corners. It's one of the reasons light spills out of a small hole in a spreading arch instead of a focus beam.
And it's come to be known as the Huygens' Principle. Christian Huygens was a mathematician and "natural philosopher," back in the 1600s. He wondered why waves behaved one way when they moved unobstructed, and behaved another when they moved through a small hole in a barrier. He noticed that light, sound, and water moved the same way, and figured they were all waves. But why were they behaving that way at all?
Huygens gave it some thought and came up with something unintuitive. He decided that every point on a wave was making its own little wavelets all the time. Those wavelets moved out in a spherical pattern, again, all the time. This is why, when a wave is restricted to one point as it hits a barrier, that point radiates out a spherical wave. Nothing special happened to that point of the wave - it just soldiered on while the rest of the wave was stopped.
But why don't we see all those little wavelets all the time? Why doesn't the shape of a planar wave turn into something round? If every point on a wave is propagating the wavelets, we see all the crests moving together, forming the same shape as the original wave. They all send out their circles, and the nearest points of those circles form a line.
So when a wave hits a barrier with a hole in it, we're not seeing anything new. We're seeing a part of the wave we couldn't observe before.