The 'fluctuation' here referred to is in the phase of the complex order parameter. To appreciate this, consider the complex Ginzburg-Landau order parameter ψ(x) in Eq. (2) of the paper by WA Little. In the mean-field approximation, the Ginzburg-Landau energy functional in Eq. (1) of the latter paper is minimised by a non-vanishing constant order parameter ψ0 below the mean-field critical temperature. To go beyond the mean-field approximation, one takes account of the deviation of ψ(x) from ψ0, this difference being referred to as fluctuation. This is done by TM Rice in Phys. Rev. 140, A1889 (1965) in the Gaussian approximation. Note that  ψ(x) -  ψ0 being a complex-valued function, it can be expressed as an amplitude times a phase. In dealing with the quantum fluctuation, one may assume the latter amplitude to be a constant, i.e. independent of x, and restrict oneself to the variation of the latter phase as a function of x. 

I do agree with the previous comment. There are only two issues I would like to add. First, usually we are dealing with superconducting fluctuations above the critical temperature of the superconducting transition Tc. In this case, we can understood the phenomenon as sporadically emerging and rapidly vanishing short-lived and very small islands of superconductivity just above Tc. The lifetime of the Cooper pairs in such islands can be estimated by using the principle of uncertainty, it is inversely proportional to the product of the Boltzmann constant and the "distance" from the critical temperature, i.e. to the product of kB and (T-Tc). That is why the superconducting fluctuations are well pronounced for temperatures slightly above Tc and strongly decay as T grows further. Second, in my opinion, the best qualitative explanation of the phenomenon can be found in the chapter “Fluctuoscopy” of Superconductors" by Prof. A, Varlamov in the book "Fundamentals of Superconducting Nanoelectronics" (edited by A. Sidorenko), Springer-Verlag Berlin Heidelberg, 2011. If you have no access to this book I can send it to you.  

Dear Mikhail, just wish to point out that there are two types of fluctuations, thermal and quantum. The two cannot be separated, except at the absolute zero of the temperature, however in the mean-field approximations quantum fluctuations are entirely neglected; at non-zero temperatures they take only account of the thermal fluctuations, and naturally thereby the interplay between the two types of fluctuations is also neglected.

Dear Dr. Behnam Farid. Thank you very much for your valuable comment.

You are most welcome Mikhail, and thank you for your kindness.

Thanks for all the answer.

But why there is fluctuations are dominant in some systems(in reduced dimensional system) and not in others (in bulk)? e.g. Why like Fluctuation-enhanced conductivity precursor effect inherent Cooper pair couldn't form due thermal fluctuation in all superconducting systems?

You are welcome.

Thermal fluctuations are associated with entropy, which at any non-vanishing temperature opposes order, and thus long-range order; the question that arises is the value of the temperature above which the entropic contribution to the free energy (the term -TS --- since both T and S are non-negative, the minus sign here is of utmost significance) overwhelms all other energetic contributions. This is not the case with quantum fluctuations, which are in essence no fluctuations at all, but fine details (a conflation of quantum and interaction effects) that are there at all temperatures but are often neglected because of the theoretical and computational difficulties associated with taking them into account. For both types of fluctuations, the dimensionality of the space into which the system is confined is of utmost significance. There is a celebrated theorem due to Mermin and Wagner [1,2], according to which long-range order (to be distinguished from topological order) is ruled out in dimensions equal to and less than 2 (there is a subtlety involved here that I do not go into, but suffice to mention that the dimensionality of the order parameter is the relevant quantity and not that of the direct space).

As for how different systems differ in their ordering properties, this is a function of many factors. One may think of the nature of the phonon modes in a system, whereby systems with soft phonon modes are more susceptible to increase in the value of the temperature than systems that do not have such soft phonon modes.  

[1] H Wagner, Z. Phys. A 195, 273 (1966).

[2] ND Mermin, and H Wagner, Phys. Rev. Lett. 17, 1133 (1966).

I can add also, Farid, that there can not be chaos in dimensionalities less, than 3, and, therefore, no birth of structures from chaos.

Dear Eugene, I take that you are not denying the existence of, say, two-dimensional dynamical billiards, many of which, such as the Lorentz gas, are chaotic systems.

Behnam Farid,

Poincare-Bendixson theoreme excludes chaos in continuous one and two-dimensional systems.

Dear Eugene, the dimension relevant to the Poincaré-Bendixson theorem is that of the phase space, whereby for a dynamical system consisting of a single particle confined to a d-dimension spatial space, one has to do with a 2d-dimensional phase space. For the Lorentz gas the dimension of the phase space is 4, not 2.

What is Lorentz gaz?

Please consult the attached entry of Wikipedia, under Hard ball system. In short, it is a particle in two dimensions confined to a region whose boundary consists of a rectangle on the outside and a circle on the inside. 

You may also wish to consider the Bunimovich stadium under the same heading.

Ps. I attach below also the link to a relevant paper on the Lorentz gas by Bunimovich and Sinai.

https://en.wikipedia.org/wiki/Dynamical_billiards

https://projecteuclid.org/euclid.cmp/1103908786

I understand all this, Behnam, but if we concentrate ourselves only on mathematics, then going from dimensionality 2 to 3 appears to be critical for physical phenomena.

I have never stated that physics in two dimensions were the same as in three dimensions. The present discussion between us originates from your earlier statement that "there can not be chaos in dimensionalities less, than 3", in response to which I wrote "I take that you are not denying the existence of, say, two-dimensional dynamical billiards, many of which, such as the Lorentz gas, are chaotic systems", in response to which you referred to the "Poincare-Bendixson theorem". My only point has been, and remains, that the dimension as relevant to the Poincaré-Bendixson theorem is that of the phase space, not the dimension of the one-particle configuration space. In short, I have been fully concentrated on the issue raised by you.

Of course, phase space, Behnam. Nobody contradicts. I want to pay your attention to the difference in topological properties of dimensionalities 2 and 3. Physical consequences follow from them.

Thanks again.

I am trying to ask simply is that, if fluctuations are same for all dimensions than why for the same material (say Nb)  in bulk there is no effect of fluctuation but in reduced dimension, it gives rise to precursor Cooper pairs? Why in bulk we don't have any short-lived Cooper pair when the material is same?