Moment of Inertia (MOI) is described in the dictionary and many physics texts (trust me, this does apply to golf) in this general, short-and-sweet manner: The MOI of an object around a particular axis describes the level of difficulty in inducing an angular rotation of the body around that axis. In Wikipedia the example of two wheels of the same mass is used. Although the wheels have the same mass, one is bigger and the other smaller in radius. The larger wheel is more difficult to spin because it's mass is spread farther from the rotational axis. Thus, the larger wheel has the greater MOI.
Clubmakers have applied MOI to their products. MOI is most clearly evident in this year's new driver offerings. Callaway, Nike, Taylor Made and others have all introduced radically- and maximally-shaped drivers providing maximum MOI. In golf terms, the large clubheads with weight spread around the outside drastically reduces twisting on impact in off-center hits. In scientific terms, the larger objects (driver heads) are more difficult to rotate around the axis (driver shaft).
Before dismissing it as simply one of those silly catch-phrases like "proactive" or "thinking outside the box," go and try some of golf's new "boxes." Maximum MOI is something to behold.