A regulator works by using a balance of pressures in the reg. In a first stage the high pressure air from the tank tries to force the seat open (called downstream force). This is assisted by the force of the mainspring which also is trying to open the seat (spring force). A third force comes into play as the diver goes deeper underwater as ambient pressure also acts on a piston or diaphragm to provide additional assist to open the seat (ambient pressure force).
These three forces are opposed by the intermediate pressure air acting on a piston or a diaphragm to force the valve closed again.
So in practice, the seat opens until the intermediate pressure increases to the level required to close the seat. This is much lower than the tank pressure (normally about 120-145 psi above ambient pressure) because the area of the piston head or diphragm is many times large than the area of the high pressure orifice and seat. Once the IP is high enough to provide enough force to overcome the downstream, spring, and ambient pressure forces, it closes the seat and prevents more air entering into the reg.
If the diver is at depth the absolute pressure of the IP will be higher as it increases to balance the increased ambient pressure, but the IP will still be the same 120-145 psi over the ambient pressure.
The intermediate pressure itself is controlled and adjusted by the strenght of the mainspring and can be adjusted with shims or with an adjustment pad that is screwed further in or out of the first stage.
In an unbalanced first stage, the downstream force changes as the tank pressure is reduced. This causes the IP to increase in a diaphragm reg and to decrease in a piston reg. This in turn means the second stage cracking effort must be adjusted a bit higher to prevent a freeflow at one extreme or the other of tank pressure.
A balanced first stage just goes one step farther and removes the downstream force from the equation by "balancing" the force on each side of the seat.
In a piston reg this means the air enters from the side in a high pressure area of the reg and does not push directly on the seat as the forces are equal.
In a diaphragm reg, a balance chamber is used in the seat carrier that is the same diameter as the orifice. So in simple terms and as in a piston first stage, the tank pressure exerts the same force in each direction and is again "balanced".
In either case this means the IP does not have to change to accommodate changes in the downstream pressure from the air in the tank. This means the IP can be stable and unchanging whether the tank is full or nearly empty. In turn this means the second stage can be adjusted for minimum breathing effort without encountering freeflow concerns at extremes in tank pressures.
More importantly, it means a much larger orifice size can be used and this increases flow rate. (In an unbalanced first stage a larger orifice means a larger change in IP and this imposes a narrow practical limit on orifice size.)