The Casimir effect was postulated in 1948 by the Dutch physicist Hendrick Casimir and it can nowadays be considered one of the one of the few macroscopic effects of the quantum mechanics. The phenomenology of the effect is simple: between two conductor plates NOT electrically charged (that for simplicity we will consider plain) leaned out a strength attraction is practiced: such strength cannot be explained with any classic phenomenon. The explanation of the phenomenon is instead not so simple: it has to do with the way according to which the void  in the quantum mechanics is defined. 

In the classical physics a region of space in which particles or fields are not present  is defined as empty; in quantum physics, because of the principle of indetermination it is impossible to guarantee the complete absence of particles and/or fields in a region of the space: the void cannot be considered a zero-energy state because of the quantistic fluctuations behaving the creation and destruction of virtual particles that, in addiction, they live weary of brief time, but finite.

Since analogous phenomenons in the experience and in the every day life don't exist we can try to imagine analogies that, because of some things, they will not be rigorous  in the description of the phenomenon in matter.  

Let's imagine the quantistic void is a state in which some little balls are continually formed and disappeared; to fix our ideas let's think of something as a bead of soap (but  supposed to be rigid) that it is born and after a certain time it bursts. Let's suppose besides that the more the ray of the little balls is little the more heavy the balls are. 

If we imagine to have a solid surface in any region of space (full of these little balls) to every fixed instant of time a certain number of little balls will bump the solid surface, originating from the right and another number of little balls will bump it originating from the left: for reasons of symmetry the two numbers will have to be average equal and therefore no strength will be practiced on the plate. If now we put two plates the one leaned out  to the other, it will happen that on the two external faces of the surfaces the phenomenon of the bump of the little balls will be analogous to what we have described before; as it regards the inside faces now we have to keep in mind we cannot have little balls having a diameter greater than the distance to which the two plates have been positioned. In this case the equilibrium among the bumps on the two faces of the plates is altered: the number of bumps from the external part of BOTH THE TWO plates is greater than the corresponding number of bumps from the inside part. Therefore things go as if around the two plates a strength that extends to approach them would act and the more bigger is the effect expected the less is the distance among the plates in examination because the little balls have been supposed to be heavier. It's still to be well underlined that the introduced analogy is well afar from being rigorous and it must be seen as a way of illustrating a phenomenon complex enough having no analogous in the macroscopic world in which we live.

Now let’s try to give a quantitative value to the effect. The module of the strength attraction among the plates depends on the surface of the plates and from their distance according to the formula:

where h is Planck's c is the speed of light d is the distance among the two plates and S is  their surface. The strength, as previously specified, is of attractive type; the two plates extend to get closer. The effect of which above is extremely small.

The recent experimental verifications [2] have found some experimental values in accord with those theoretical in about the 15%.
This effect is synthetically represented by the following figure [3]

This effect has also allowed a lot of and strong speculations brought in articles like Casimir Effect and antigravity of M. Nardelli [4] or The engineering of the wormhole of John Gribbin [5]. 
 
In conclusion, if two conductor plates, at the same potential, are sufficiently approached, a strength manifests that currently it comes to be attributed to quantistic fluctuations of energy that, thanks to the principle of indetermination by Heisenberg, it cannot be null. And this is one of the few macroscopic effects, if it's not the only one, of the actual quantistic mechanics. From here even its big importance for technological applications of avant-garde.