As a very crude analogy, it takes more air to blow a feather across a table than a pen. The friction force translates to the energy converted from the air pressure to motion. To move a more stubborn object, higher pressure is needed. The higher pressure means more air will leak around the object resulting in a higher volume of air needed.
As for the mechanism behind the turbine speed, the rotation of the turbine is what generates electric potential to drive the load. The interaction of the generator's magnets and coils effectively couple the turbine shaft to whatever is using the power. As more load machines connect to the grid (couple to the turbine), the turbine will become harder to turn. It thus takes more work (steam) to keep the turbine spinning the same speed. Power is torque times speed, so if you must maintain speed, the torque must vary.
It's important that the turbine remain the same speed because that controls the output voltage and frequency, and the load machines are designed to operate in a specific window.