Basically physics is science because it can not be absolutely precise. It provides models and those models fit somehow to reality. Now imagine that you model motion of Earth in the gravitational field of Sun. Using Newton theory of gravity you can solve this two-body problem exactly. But you have neglected influence of Jupiter! You can not solve 3 body problem exactly so you can try for example perturbation method considering that the solution of two body problems (Sun-Earth and Sun Jupiter) you have is quite good, but the Jupiter will have just small influence on motion of the Earth. But Jupiter was always there ( for about 4G years). The same is situation in quantum mechanics (what you are probably asking about). You are able to solve some problem (Hydrogen atom e.g.), neglecting some hopefully small term (e.g. magnetic interaction of electron and proton). Having the solution without small term you can try to correct your solution by adding small term back supposing that solution with neglected term will differ from previous solution just a little. For such cases the perturbation theory works.

Dear Jaroslav Tóbik ,

Thanks for your answers!

I do agree with your points. As there are two types of Perturbation theory(PT). One is Time independent PT(TIPT) and the other is Time dependent PT(TDPT). For instance, In case of TDPT, the Hamiltonian is written like H (r,t) which is clear that the perturbation is occurring is some sort of time. However, I am confused about the TIPT that how perturbation is happening in no time because the name says Time independent. Do you have some more convincing points so I can make it clear to me. Thank you

Dear Qamar Wali,

see : "sudden" perturbation.

http://www.tcm.phy.cam.ac.uk/~bds10/aqp/handout_dep.pdf

Perturbation theory can refer to many different techniques in different fields, for instance differential equations, hamiltonian mechanics, operator theory... Generically you may have situations in which you have a good knowledge of the system, or a situation in which your system is easy to describe and you want to know the behaviour of the system in a more difficult situation by spliting your system in your known part plus a perturbation that may or may not be time dependent. For instance in Hamiltonian mechanics you may have a reference hamiltonian that is integrable and you want to know what happens when you perturb the system, you may ad a time dependent or a time independent perturbing Hamiltonian. It does not mean that your system won't depend on time, it's is just that the Hamiltonian that you are adding doesn't depend on time.