Shortly explained it is the lattice plane where the electron density variation in between is maximal compared to other planes. If all atoms or ions are somehow aligned in or close to this plane and the volume between two adjacent lattice planes is nearly empty the "reflection" of this plane has a high intensity. The stronger the electron density variation the higher the intensity for this plane. In mathematics it is expressed by the hx+ky+lz in the exponential term of structure factor. As you can see, it is the scalar multiplication of a direct vector (atom coordinate [x,y,z]) with a reciprocal lattice vector (hkl). It results in the fact that not always low indexed hkl are strong. For a more arbitrary atomic distribution (crystal structure) also an interference hkl=119 can be one of the strongest reflection in an diffractogramm.

Please, take a look to the file below, from wikipedia:

Besides, there are actually three very nice discussions on the topic following the links below:

http://physics.stackexchange.com/questions/170386/understanding-braggs-x-ray-diffraction-and-why-light-is-treated-as-a-single-ray?rq=1

http://physics.stackexchange.com/questions/121261/bragg-diffraction-and-lattice-planes?rq=1

http://physics.stackexchange.com/questions/130950/what-exactly-are-crystal-planes-and-how-do-they-reflect-x-rays?rq=1

Shortly explained it is the lattice plane where the electron density variation in between is maximal compared to other planes. If all atoms or ions are somehow aligned in or close to this plane and the volume between two adjacent lattice planes is nearly empty the "reflection" of this plane has a high intensity. The stronger the electron density variation the higher the intensity for this plane. In mathematics it is expressed by the hx+ky+lz in the exponential term of structure factor. As you can see, it is the scalar multiplication of a direct vector (atom coordinate [x,y,z]) with a reciprocal lattice vector (hkl). It results in the fact that not always low indexed hkl are strong. For a more arbitrary atomic distribution (crystal structure) also an interference hkl=119 can be one of the strongest reflection in an diffractogramm.

The Gert´s answer is very sound and compact. A good reference for further studies is the Kittel Ch. book "Introduction to Solid State Physics". In a few words: the intensity of XRD peaks depends of the light interference of radiation dispersed for the group of atoms forming the "base"  of the crystal structure. These intensities also depend of second order effects as microabsorption (heterogeneity of powders), mosaic structure, extintion, textures, defects, instrumental effects, etc.

By the other hand, the applications of these high intensity peaks are diverse. The most classic is in phase identification. The search systems as JCPDF (Hanawalt method) is based on the three more intense peaks for each phase, followed by other peaks by intensity order. For quantitaive analysis, best peaks are the most intense because they achieve a great sensibility with reduced errors. Other applications could be in monocromators, intensity standard samples. For this the classic books are Cullity´s and Klug&Alexander´s

 Only a short extension (to make it more irritating :-) ). There is no "real" plane you are asking for. This plane is a mathematical abstraction of the inherent translation symmetry. Where there is no plane there is no reflection... and frankly speaking also this is correct :-(. As usual, everything is more complicated than commonly explained.

However, the definition of planes is not totally useless, since macroscopically they become visible as facets on a crystal. However, microscopically (in nanoscale) these planes are really rough. 

As Gert Nolze and others have remarked, the whole concept with "planes" and "reflections" can cause utter confusion because it is only an ingenious "invention" (Bragg) to calculate in an easy way where to expect constructive interference based on the lattice geometry only (the structure may be such that the intensity is zero there) . Very many people get the idea that the lattice planes are real planes of atoms -- in general they are not (think of bulky proteins...). Therefore, a search for a certain special atomic arrangement (an atomic plane with these indices attached to the strongest reflection) is misleading.  

In comparison, facets are indexed with the lowest hkl:s, so that for instance a cubic crystal may have faces of the type {100}, while reflections of the type {100} still may be absent (for a certain space group). The very structure dictates what the intensity will be. The indices of faces only give information of the relative orientations (but do not mix up {hkl} with ). Although the faces have low indices, it can indeed happen that the strongest reflection occurs for unexpectedly high indices, as Nolze commented on -- found for special atomic arrangements.

The XRD reflection which has maximum intensities means that the diffracted planes which produce this maximum intensities contain the highest number of atoms which possess   the highest n umber of electrons in the unit cell of the examined materials. 

The peak intensity shows the  extent of crystallinity of the particular plane.  As crystallinity is a relative term and  not absolute.  In comparision with the available samples, total  sum of the various prominent peaks intensity one can calculate the crystallinity.