What is reason for reversible and irreversible solution?

"Reversible solution" and "irreversible solution" are meaningless terms.

Please refine your question.

Perhaps you are referring to chemical reactions....

Some chemical reactions go all the way to completion, but some reach an equilibrium where there is a forward reaction (as indicted by the way the chemical equation is written) and the reverse reaction which occur at the same rate and therefore, are in equilibrium.

Consider a reaction which is irreversible. Starting with the hypothetical reactants A and B, product C is formed spontaneously. But if you started with compound C, it would never spontaneously form compounds A and B. The reaction of A and B to make C is irreversible.
A + B --> C
C --> no reaction

Consider the reaction where A and B make C. But if we start with C we observe that over time some A and B are formed. Eventually, there will be a point in time where the relative concentrations of A, B and C are constant. This is an example of a reversible reaction which has reached equilibrium.
A + B --> C
C --> A + B
A + B <==> C .............. chemical equilibrium

There are also cases where seemingly irreversible reactions can be forced to go in the opposite direction. The reverse reaction does not occur spontaneously, but will occur if energy is added from an outside source. Consider the combustion of hydrogen in oxygen to make water. Water does not spontaneously decompose into hydrogen and oxygen. Therefore, the formation of water is irreversible. But, by applying an outside source of energy it is possible to force the reaction to go in the opposite direction. Such is the case with the electrolysis of water. Water can be forced by applying an electric current to decompose to form hydrogen gas and oxygen gas.
2H2(g) + O2(g) --> 2H2O(g)
H2O(g) --> no reaction
2H2O(l) --electricity--> 2H2(g) + O2(g)

What do you mean by a reversible ( or irreversible) solution?