The Casimir effect is the result of the unknown properties of space postulated and discovered by Einstein with special and general relativity. If you have read the Wikipedia article (Casimir effect) describing the effect you would know that one of the suspected causes of it is the zero point energy of space. The only way this could be true is if spacetime in general relativity was more than just an elastic manifold but an object with properties all its own. Thanks to CERN and particle physics, the most important property of space has been discovered: The Higgs boson
Because only the physicist or avid hobbyist would be interested in reading all the facts behind the discovery of the Higgs boson, only the postulated results of successful completion of this project will be discussed. The first most obvious benefit to discovering the responsible mechanism for the Casimir effect is the ability to use the properties of space to move objects at will. Imagine how much different technology would be if we discovered that we no longer needed internal combustion engines to move our automobiles. All other benefits from this research are on a much deeper level so we will leave it up to all those interested to try to discover these benefits, maybe even by simply using their imaginations. A good place to start reading is here: Quantum entanglement.