Put a small solid piece of steel in water and it sinks. Watch a huge steel ship leave a harbour and the obvious explanation—heavy things sink—falls apart. The ship is heavier than the little piece, but heaviness alone is not the deciding factor.
A floating vessel pushes water aside. That displaced water determines the upward buoyant force. The ship's hollow shape allows it to displace enough water to support its weight before water comes over the sides.
Water pushes upward as well as sideways
Pressure in still water increases with depth. The lower parts of a submerged object therefore experience greater pressure than higher parts. Adding up those pressure forces produces a net upward force.
Archimedes' principle describes its size: the buoyant force equals the weight of the fluid displaced. For a ship resting steadily afloat, that upward force balances the weight of the entire vessel and everything aboard it.
The displaced water does not need to be trapped in a visible bucket. It is the volume of water that would occupy the submerged space taken up by the hull. A ship's waterline tells us how much of that space lies below the surface.
The hollow shape changes the comparison
A solid steel block contains a large mass in a relatively small volume. Even when completely submerged, it cannot displace water weighing as much as itself. It sinks.
A ship spreads its steel, cargo and machinery around a much larger enclosed volume, much of which contains air. Its average density, considering that overall volume, can be lower than the surrounding water's density.
The air does not provide a mysterious extra upward push from inside. Keeping water out lets the hull exclude a large volume of water without adding an equally large mass. Shape and watertightness are doing essential work.
More cargo means a deeper waterline
Add cargo and the vessel must displace more water to balance its greater weight. It settles deeper. There is a limit to how much it can do this while retaining adequate safety margins and stability.
Water density also matters. Salt water is generally denser than fresh water, so a given weight can be supported by a slightly smaller displaced volume. The same loaded vessel therefore tends to sit differently when the surrounding water's density changes.
Temperature and dissolved material can affect density too. For a large ship, apparently small differences deserve careful engineering attention.
Floating is not the same as being stable
A vessel can have enough buoyancy and still be vulnerable to capsizing. How its weight is distributed, its hull shape and how the buoyant force shifts when it tilts all matter.
Flooding creates another problem: water entering spaces intended to remain dry changes both weight and buoyancy, and moving water inside can undermine stability. Watertight compartments help manage those risks.
The steel ship has not defeated the rule that steel is denser than water. It succeeds because the relevant object is the complete vessel. Water supports the weight of what the hull carries by pushing back against the water the hull displaces.