In the final video of the S.P.E.C.I.A.L. series that has been releasing in anticipation of Fallout 4, luck is exemplified and explained.
The video depicts several instances in the Fall0ut universe where having a great luck stat might help you out as the player. These instances vary from getting critical hits on a tough enemy to what the player may find in a chest. The video ends with a quick run down of some of the perks that having a luck stat enable.
In playing previous Fallout games, I never put too much emphasis on luck, preferring to place points in stats with tangible benefits as opposed to something which may help at some point in the future.
Fallout 4 is launching on Nov. 10 for the PC, Playstation 4, and Xbox One. The Xbox One version of the game comes with a digital download for Fallout 3, capable of running on the Xbox One.