Archimedes’ Principle says that an object immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.
Archimedes was one of the greatest scientists of the classical age, contributing a wide field of work in engineering, mathematics, and physics. The physics idea that bears his name, Archimedes Principle, deals with the buoyant force, which is an upward force that a fluid exerts on any object that is immersed within it.
When an object is placed in water, some of the water is pushed out of the way to make room. This water tries to move back into its previous location, pushed by the force of gravity that is pulling it down towards the Earth—in other words, its weight.
If that immersed object was a cube, then the force of water pushing on the four sides cancels out, leaving just the water pushing up from below, and possibly also pushing down from above if the object has been fully submerged. Either way, the pressure within the water increases with depth (this is why your ears pop if you go to the bottom of a pool, but not if you dunk your head just under the surface), so there will be more pressure pushing on the bottom of the cube than on the top. This extra pressure translates to extra force, and is the origin of the buoyant force.
(Note: a lot of people have heard of the Eureka! [Greek for I have found it!] story, where Archimedes discovered that the volume of water displaced by an object is equal to the volume of the object itself. This made measuring the volume of irregularly shaped objects simple, since they could just be immersed in a full container and the volume of water that spilled out could be measured. This is an important idea, but not exactly the same as Archimedes Principle, which deals specifically with the force exerted by that displaced volume.)
Floating objects displace their own weight of fluid (so the forces are balanced)
An object that is floating has its downward force from gravity exactly balanced by the upward force of buoyancy. Put another way, as an object is lowered into water it will begin to float once it has displaced an amount of water that weighs just as much as the entire object. This is why boats are able to float even though they are made of very large amounts of metal: a one ton brick of metal will sink, but if that metal is spread out into a bowl shape it will displace one ton of water before it sinks entirely below the surface, and therefore will float.
Glaciers work the same way: if you drop a glacier into the water it will sink until it has displaced its weight worth of sea water. Glaciers are typically formed from snow melting and re-freezing, which means they are fresh water—in addition, it turns out ice forming from sea water has a tendency to force the salt out of the forming ice crystal. In general fresh water ice is a bit less dense than fresh liquid water, and salt water is a bit denser than fresh water, so this means glaciers tend to be less dense than the sea water they are in: as a result, they float. The density isn’t too far off, though, which is why most of the glacier tends to be submerged: it takes most of the glacier’s volume to displace a weight of sea water equal to the total weight of the glacier.
There is a lot of ice resting on land, like on Antarctica, which will raise the sea level as soon as it melts
So the floating glacier displaced its weight worth of water, even though some of the glacier is still above the water surface. If the entire glacier melted to water, it would still weigh the same, and so it would still displace the same amount of volume. So, the glacier won’t displace any more water once it melts, which means the net result is no sea level rise.
Well then what’s the big problem with melting glaciers? It’s actually not the glaciers that are the problem, but rather the huge amounts of ice that are currently sitting frozen on land. Antarctica is considered a continent not because it’s one big chunk of floating ice, but because it’s a big chunk of land rising out of the sea floor that happens to be covered in ice and snow. In fact, Antarctica has 90% of the ice in the world, and most of that is sitting on land.
Now Antarctica is quite cold, so the worry isn’t that its ice will start melting soon—although if it did, that would raise the sea level by some 200 feet, which is enough to cover the entirety of the state of Florida (and many other places). Smaller amounts of ice melt from places closer to the equator would still be enough to ruin coastal cities, which is why we have to do whatever it takes to begin combating climate change now.
Bonus physics—Glacier colors
Sometimes glacier ice that is especially pure will appear blue—that is, it was formed under higher than normal pressures so there are no air bubble imperfections. This can happen if the ice forms underwater and then is dislodged so that it can float to the surface. The reason why glacial ice looks blue is the same reason the ocean itself looks blue, but that’s for another post!