equilibrium constant is just a fancy way of saying that the ratio of products:reactants is always the same value.

give example, write out the chemical equation.

the concentration of a pure liquid or a pure solid is effectively the density.

And not reciprocal of density? The denser the substance, the higher its amount in the volume unit, thus the higher the concentration.

what "reference-value"?

the unit of equilibrium constants varies from reactions to reactions. There is no fixed unit. For gaseous reactions, we use partial pressure to denote concentration, thus the unit of the equilibrium constant for "N2O4(g) <-> 2 NO2(g)" is bar (or any other unit of pressure, eg. atm).

What is the unit of equilibrium constant for the Bon Haber Process?
N2(g) + 3H2 (g) <-> 2NH3 (g)

[K] = [bar]²/[bar]⁴ = [bar]^-2

From the termodynamical point of view you should use not concentrations but activities - which are dimensionless. Thus whole discussion should be pointless. But - as activities are seldom used - equilibrium constant has dimension.

After posting this question on some other forum (and after reading answers posted there) I suppose that your book uses these reference values just as a trick to make "equilibrium quotient" dimensionless - which is important especially when you have to take a log out of it.

Note that dividing all pressures or concentrations in the quotient by the same "reference value" equal to 1 unitofyourchoice you will remove dimension, not changing the value of the equilibrium constant.