The Earth's molten outer core is a giant natural magnet, and creates a magnetic field. The needle in your compass is a little magnet itself, and it tries to position itself so that the north pole of the compass points to the south pole of the Earth's core and vice-versa. This allows you to know which direction is because of where your needle is pointing.

Interestingly, the pole of the Earth's magnetic field is not in the same place as the pole of the Earth's rotation; it's off by a few hundred kilometers. Your compass points to the magnetic pole, not the rotational pole. You need to account for where you are on the globe if you want to take a truly precise measurement of which way is north because of the difference in direction to the rotational pole versus the magnetic pole. For the most part, you using a compass don't need to worry about that.

Incidentally, if you want to check your compass, you can also use the sun and moon to navigate. They rise in the east, set in the west, and (if you live in the northern hemisphere) when highest in the sky they are to the south. If you ever go to the southern hemisphere or live there, then the rule is the same except that they will be in the north at their highest point in the sky.