CERN's aim is to conduct pure and theoretical research of a fundamental character to "answer questions about the universe." CERN's political agenda is to be apolitical. Their 1954 Convention mandates that they shall bring nations together for collaborative research and technology advancement while providing education and training at all levels for all nations to provide for the next generations of physics researchers. Additionally, CERN's mandate prohibits "work for military requirements" and stipulates that all research, results and technology shall be publicly available, disseminated, provided and transferred. The four prongs of their Convention mandated mission are:
* Research: Seeking and finding answers to questions about the Universe
* Technology: Advancing the frontiers of technology
* Collaborating: Bringing nations together through science
* Education: Training the scientists of tomorrow
As to CERN's influence on science, CERN has added massively to the understanding of the particle physics from their earliest experiments in particle acceleration to their recent collaborations with Italy on the mysterious nature of oscillating neutrinos to the above mentioned building and currently accelerating start-up of the Large Hadron [particle] Collider (LHC), with its four interior experiments devoted to discovering the Higgs boson, which is expected to explain the existence of baryonic (ordinary) matter and the origin and nature of dark energy and dark matter, which comprises roughly 70 percent of the universe. LHC's recreation of the primordial soup present at the earliest moments of the universe is expected to revolutionize the Standard Model of Physics and make it obsolete by turning up altogether new physics.
And as if that weren't enough, once LHC really gets rolling in 2010, CERN may influence science by creating mini-black holes and strangelet particles that may devour the universe from CERN outward or propel the universe into another parallel universe, respectively, with the odds that that new universe would not be so friendly to baryonic matter (you, your chair and your kitty cat and doggy), so that we'd all find ourselves missing.
The European Organization for Nuclear Research is best known for its Large Hadron Collider that has been so much in the news lately. Its aim (which the LHC is supposed to further) is to better understand the basic parts of matter -- the subatomic particles. Politically, their agenda is to push for further research of these partcles.
CERN influences science in a major way in that its work helps to influence our understanding of the basic building blocks of matter. That much is positive in that it advances our knowledge. What may be negative is the way that CERN pushes for hugely expesive projects, such as the LHC. Their type of science consumes such tremendous quantities of resources that, you can argue, the take resources away from other important projects.