Intuitive

The Casimir effect is an observed attractive force between two uncharged metal plates due to quantum vacuum fluctuations.

The quantum vacuum fluctuations can be interpreted as virtual particles that permanently pop in and out of existence in the vacuum.

The Casimir effect is a prediction of Quantum Field Theory.

• Being pushed around by empty space: The Casimir Effect by Brian Skinner

Concrete

• For a nice description see chapter 19 in Sleeping Beauties in Theoretical Physics by Thanu Padmanabhan
• http://www.stat.physik.uni-potsdam.de/~pikovsky/teaching/stud_seminar/ajp_casimirforce.pdf
• https://physics.stackexchange.com/questions/26877/regularization-of-the-casimir-effect

Abstract

• The Casimir Effect and the Quantum Vacuum by R. L. Jaffe
• K. A. Milton, J. Phys. Conf. Ser. 161, 012001 (2009); The Casimir Effect: Physical Manifestations of Zero Point Energy (World Scientific, Singapore, 2001);
• M. Bordag, U. Mohideen, and V. M. Mostepanenko, Phys. Rep. 353, 1 (2001);
• M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Advances in the Casimir Effect, International Series of Monographs on Physics (Oxford University Press, Oxford, 2009).

Why is it interesting?

The Casimir effect is an experimentally verified phenomenon that shows that the vacuum is not really empty, but filled with vacuum fluctuations.