What precisely is \$R_{ds(on)}\$?
To answer your second (sort-of) question first, you would normally operate a MOSFET in the ohmic (aka linear or triode) mode when it is used as a switch. The voltage drop across the MOSFET is more-or-less proportional to the drain-source current. 

In the saturation region, the current through the MOSFET is more-or-less independent of the drain-to-source voltage- it 'looks' like a constant current source or sink once the voltage across it is great enough. Image from Wikipedia. 



Rds(on) is the slope of the above curve (well to the left of the red curve). As you can see, the slope depends on Vgs. It also depends on temperature, which is typically stated to be Tj = 25°C. 

Here is how a typical small high-performance MOSFET behaves: 



The Rds(on) resistance is fairly constant up to several amperes. It also has a strong temperature dependency, so at 150°C it may be 70% higher than at room temperature. And, like most specs, the typical curves don't represent the guaranteed limits. The difference between typical and the worst-case (hot) Rds(on) may be as much as 2.5:1 so it is better to be conservative when specifying parts.