If you look closely at a typical passenger cabin window, you’ll see three panes, typically made of acrylic materials. The purpose of the innermost pane—sometimes called the scratch pane, but I like to call it the smudge pane - is merely to protect the next one.
The middle pane (with the breather hole in it) and the outer pane are more important. Generally speaking, as an aircraft climbs, the air pressure drops in both the cabin and the outside air—but it drops much more outside, as the aircraft’s pressurization system keeps the cabin pressure at a comfortable and safe level. This means that the pressure inside the aircraft during flight is typically much greater than the pressure outside.
It turns out that itsy bitsy hole in the bottom of your airplane window is actually a very important safety feature. It's all-too-easy to let your mind wander when you're confined to a tiny box of space while hurtling 40,000 feet in the air at hundreds of miles per hour, but rest assured: every single window on the airplane has the same hole. More officially, it's called a breather hole and it's used to regulate the amount of pressure that passes between the window's inner and outer panes. In short, the system ensures that the outer pane bears the most pressure so that if there were a situation that caused added strain on the window, it's the outside panel that gives out (meaning you can still breathe).
The breather hole also keeps the window fog-free by wicking moisture that gets stuck between the panes. After all, half the fun of an airplane ride is the in-flight scenery shots. Mystery solved.