Cool, So the GECK is this computer that looks like a briefcase, that can rejuvenate a very large area from an atomic bomb blast? Please enlighten me! I don't understand.

In classic Fallout (Fallout 1 and 2). The GECK was a briefcase computer, kind of like the one that the US President can use to launch the nukes, that was only to be opened in the event that the Vault was opened. It contained blueprints for building things on the surface with local materials, plans of how to safely dismantle the Vault to use it's systems above ground, codes for the Vault computer to produce new Vault suits for outdoor wear etc.

In Fallout 3 they made it into some machine that does something that can remove radiation or something but still keeping the same appearance as a briefcase computer.

In Fallout 3 it apparently has some terraforming powers or something. Its never really explained how exactly this works.