Physically the resistance is determined by how freely the electrons can move in a material and how difficult it is for them to move between the atoms in the material. It varies from vary easy in a good conductor, such as copper, to virtually impossible in a good insulator, such as glass. A resistance does not have to obey Ohm's law which typically defines a linear resistance (resistance constant over a range of voltage). So a resistance can be non-linear, such as in semiconductors, and still be resistance, since it impedes current flow . The incremental resistance of a non-linear resistance can be defined as the first derivative (dv/di) of Ohm's law at a particular point on the voltage/current curve as Mike noted.
Note that the definition of resistance is properly applied to an impedance that is independent of frequency and dissipates power. (I make that distinction because certain impedances, such as a transmission line, can have an impedance independent of frequency but dissipate no theoretical power). Reactive elements such as inductors and capacitors can also reduce the flow of current, but that impedance is frequency dependent and is called reactance. In general any combination of resistance and reactance is called impedance.