It's used when discussing propulsive efficiency, as it's a proxy measurement for how much "work" each blade is doing. Because propeller/rotor blades are just high-aspect wings, if you have high disc loading your blades are at a high lift coefficient which means they'll be incurring lots of lift-induced drag which increases your power requirements.
Solidity in the same context refers to the amount of volume within an actuator disk that's occupied by actual solid material. If you have a 4-bladed rotor and you move to a 5-bladed rotor, all else equal, you've increased your solidity.
There are many many equations, and as most things in fluid mechanics you can get as deep into the weeds as you want. As a starting point, have a look at the wiki article for Blade Momentum Theory[0]
Let's take a contrived example. I have a 4 engine high wing airplane with 2 bladed 55 inch props on each engine with 100kg force (1 kg-f is equal to 9.8 N) thrust per engine.
Now, I need to make that a low wing airplane so need to change to 22 inch blades with the same thrust and I don't want to change engines. So I want to add more prop blades. How many more blades do I need to add?
1) 100kg is a measure of mass, not force. Thrust is a force, not a mass. But let's say you have 100N of thrust per engine.
2) Why would changing from a high-wing to a low wing monoplane require you to add prop blades?
But to get to the heart of your question: You want to reduce the prop diameter (ground clearance perhaps? The engineer in me asks why you don't just make the landing gear taller) and not change the engine. You don't actually have to add blades (maybe). You could also just make the existing blades fatter, or change the airfoil, or increase the propeller RPM. Lots of ways to attack that.
But, playing along that adding blades is the only way:
1) Take your existing high-wing plane and calculate power required for all phases of flight: Take-off, climb, cruise, etc.
2) Take your new low-wing plane with its smaller prop diameter and work backwards to ensure you can actually meet the power requirements to stay aloft through your envelope. Adding blades reduces efficiency because the blades' wakes interfere with each other so you'll have to dig into some experimental data based on the prop of your choice. Much depends on blade pitch and washout.
Very likely you will need to increase the RPM (if your engine can deliver enough power) or change engines to a more powerful model because your props are now less efficient.
Such is the nature of aircraft design - almost nothing can be changed without affecting something else.