Strength is the first of what the Fallout acronym S.P.E.C.I.A.L. means. Bethesda was kind enough to give us this part 1 video detailing how and why it matters. Expect parts 2 through 7 to explain everything else. Of course it wouldn't be Fallout without retro black and white stylized infomercial cartoon to tell us what we can do right and wrong.
The simple breakdown: Strength will let you carry more, which in a game like Fallout is a huge benefit. There are few things quite as annoying as having to dump a bunch of scavenged loot and come back for it some time in the future. Strength will also give you more damage with melee weapons and your fists. Strength brought along special options in discussion in Fallout 3, and we may see that return for some intimidation factor this time around. We will find out that and more on November 10th.