These diagrams are temperature composition diagrams for systems of two partially miscible liquids (that is, liquids which do not mix in all proportions at all temperatures). The interpretation of these diagrams is in principle precisely the same as that of liquid-vapour diagrams. A typical example of such a diagram looks like this (note the x axis is labeled with the mole fraction of B in the entire system):

Suppose that a sample of pure liquid A is at temperature T on the diagram. If a small amount of B is added, it will dissolve entirely, and the system remains a single phase. This corresponds to the portion of the plot to the left of the point where the blue line meets the x axis (low mole fraction of B). If more B is added, a point is reached where no more will dissolve, and the system now consists of two phases in equilibrium with each other. The major phase is A saturated with B, the minor phase is B saturated with A. The two phase region is that between the two lines.
If we consider that sufficient B has been added to take the composition of the system to I, then the state of the system is represented by the point Φ. The compositions of the two phases (A saturated with B and B saturated with A) are given by the points Φ’ and Φ” respectively, and their relative abundances are given by the lever rule.
When more B is added, some A dissolves in it until it is saturated. The compositions of the two phases in equilibrium remain Φ’ and Φ”, but their relative abundances will alter.
Eventually, a stage is reached where there is sufficient B present to dissolve all the A, and the system reverts to a single phase (to the right of the green line). Addition of more B after this merely dilutes the solution.

Note that the composition of the two phases in equilibrium at a given mole fraction of B is dependent upon the temperature.

For a mixture that has a phase diagram of the above form, raising the temperature increases the miscibility of the two liquids (narrows the range of compositions at which two phases exist).

Above a certain temperature, TUC, the upper critical solution temperature, the liquids are miscible in all proportions. Phase separation does not occur above TUC.

This may be rationalised as the thermal motion at and above this temperature being sufficient to overcome any favourable interactions between like molecules that would favour phase separation.

Not all systems show an upper critical solution temperature. Some show a lower critical solution temperature, TLC, below which they mix in all proportions but above which they can form two phases. The rationale behind this is that miscibility may be increased by formation of a weak complex between the two species at low temperatures, but that at higher temperatures, this complex is broken apart by the thermal motion of the particles.  The diagram for such a system typically has this form.

Some systems have both an upper and a lower critical solution temperature. (One of the best known examples is a water/nicotine mixture.) The phase diagram for such a system has this appearance:

Only within the area enclosed by the two lines can two phases exist in equilibrium.