In an ideal solution of two liquids, both components obey Raoult's Law. However, it has been experimentally observed that, for real solutions at low concentrations, although the solvent (the major component of the solution) usually obeys Raoult's Law, the solute (the minor component of the solution) does not. The vapour pressure of the solute is proportional to its mole fraction, but the constant of proportionality is not the vapour pressure of the pure substance. This relationship is defined in Henry's Law:

Note the solute is labeled as substance B to avoid confusion with the solvent, labeled A. x_B is the mole fraction of the solute, and K_B is an empirically determined constant with the dimensions of pressure, chosen so that on a graph of the vapour pressure of B against its mole fraction, the Law gives a tangent to the experimental curve at x_B = 0 :

Mixtures for which the solute obeys Henry's Law and the solvent obeys Raoult's Law are called ideal-dilute solutions. Note K_B may be greater or less than p_B*.

The reason that the behaviours of solvent and solute differ so markedly at low concentrations is intuitively quite obvious. The solvent is in large excess, so solvent molecules are likely to be surrounded by other solvent molecules. Their environment is very much like that of the pure liquid, and consequently the behaviour of the solvent is very like that of the pure liquid. The solute, on the other hand, is in low concentration, so solute molecules are likely to be surrounded by solvent molecules. Thus their environment is quite different from in the pure solute, and consequently their behaviour is greatly modified.

Exceptions arise when the solvent and solute are of very similar structure. In this instance, though the solute molecules are still surrounded by solvent molecules, their environment is not dissimilar to that in pure solute, their behaviour will not be greatly altered, and both components of the mixture will tend to obey Raoult's Law.
This also explains why the greatest deviations from ideality are observed for strongly dissimilar liquids.