Awesome question! In fact, there's a cool story behind this - the ancient Greek scientist and mathematician Archimedes was thinking about a question similar to yours while he was taking a bath. He suddenly had a realization, and was so excited that he went running naked through the streets shouting "Eureka!"

This story is a little silly, and is probably exaggerated, but the idea that Archimedes had was correct. What was his idea? It had to do with something called buoyancy, or what happens when you put something in a fluid (like water). When you put an objects underwater, some water has to move out of the way to make room for it; this is called displaced water. Archimedes' principle says that when this happens, the object gets pushed up with the same with the same weight as the displaced water.

This is how boats float: when you put a boat in water, it has to push some water out of the way. But as the water is pushed out of the way, the boat feels an upward force equal to the weight of that water. If the boat pushes enough water out of the way, the upward force manages to balance out the force of gravity pulling the boat down, and so the boat floats.

But! What happens if you start filling the boat with water? Well, the boat becomes heavier, so it needs to sink lower to push more water out of the way. Eventually, the boat gets so full of water that even if it sinks completely it's unable to push enough water out of the way to stay afloat, and it sinks. So it's important that boats be full of air, not water! Either that, or the boat needs to be made of something light, like wood or plastic, that floats on water.

Boats float because although they are heavy, they are still less heavy than the amount of water needed to fill the boat would be. This is something that is called density: the amount of weight in the amount of space that it takes up. If something is denser (higher density, more weight for space) than water, it will sink; otherwise, it will float.

The design of boats is what makes them float, even though they are really heavy. As you might know, most boats have a metal shell that is filled with cargo and people, but also a lot of air. The air is light compared to the water below, so the total weight of the ship, including the air, is less than the water below it. This makes the boat float on top of the water!

A heavy rock sinks, but a boat, equally heavy, doesn't! Neat! So what gives? The Biggest factor is the contact area between the boat and the water (the area where the boat and water touch). The secret to floating boats is a problem of spreading the weight over a large area of water. If you think of a bunch of water molecules trying to hold up a boat, they're pushing against the boat to keep it on top of the water. If the contact area between the water and the boat is larger (a large area of the boat is touching the water), more water molecules can push against the boat, so they can keep it afloat. You can think of it like lifting furniture. You might not be able to lift it alone, but if several people help out, each person lifts a part of it. Boats tend to have big flat surfaces on the bottom (the hull of the boat), which helps them float. Although they're heavy, they spread their weight across a large surface in the water.

There's a second, and more complicated, part of floating that has to do with pressure. If you've ever tried to swim to the bottom of the deep end of a pool, you know that your ears get sore unless you equalize the pressure in them. This is because the pressure of a fluid (like water) increases as you go further down. If there's a big object in water, the bottom of the object (in deeper water) tends to get pushed up by the higher pressure, and this also helps it float.

When a boat is in the water, there are two forces acting on it: 1) weight (pushing down) and 2) buoyancy (pushing up). The boat floats in the water because the two forces are balanced (weight = buoyancy). The "weight" force exists because of gravity acting on the boat. The "buoyancy" force is a little more complicated- it exists because the boat takes the place of some of the water it is floating in. The weight of this water is more than the weight of the boat (even if the boat is made of steel!), so the boat floats.