Genosha was a base for the Brotherhood of Mutants.
Genosha was an island built to serve as a base of operations for the Brotherhood of Mutants. It contained an office for Magneto and cells for prisoners like Senator Kelly.
After Magneto's arrest and his subsequent break-out, it is unknown if Genosha was ever utilized again by the Brotherhood for its operations.
However, it appears that by the time of X-Men: The Last Stand, Genosha was abandoned in favor of Magneto's new base of operations - the Forest.