To prevent "things mankind is not yet ready to use" from being misused.
The Consortium has existed for a very long time. Almost nothing is known about them, except for the fanaticism to their purpose.
It was founded by Trevor Grant around the same time he started Eureka. The original purpose was to build a time machine to prevent the Manhattan Project, and thus the atom bomb, from ever existing by deporting Einstein. It was named due to the fact it was originally composed of a "consortium of scientists".
They have a level of influence that covers almost the entire American government, as well as agents in several high-ranking positions across the globe. The Consortium currently has all the information Global Dynamics has about the Artifact (one of the "things mankind is not ready for"), due to Beverly Barlowe and her recent escape from Eureka. Beverly is seen speaking to a shady character using a voice distorter in the season 1 finale. It is unknown who this is, but it is implied within the scene that the person works from Global Dynamics using the same IP Phone found in Nathan Stark's office.
In an alternate timeline, Beverly quit the Consortium, so it is assumed that the Consortium will let its members leave the group without having them killed. However, given her status as the daughter of two original members, it is possible that she was granted special privileges.
In the new timeline created after Carter, Lupo, Fargo, Henry, and Allison go into the past and return to a "different" Eureka, Beverly Barlowe claims she is a member of a group who watch for weapons that mankind should not have/use. It is confirmed that this is The Consortium.