Mostly they affect your initial skills and your aptitude for skills (you get 1-3 stars, I believe that just makes it level faster). But some of them have major effects beyond that. Notably speed affects your walking/skiing and running speed, while endurance reduces the penalty you get for carrying stuff and makes you more resistant to fatigue. Few of them (like will) affect how well you can resist falling asleep or passing out from pain. And I have heard eyesight and hearing make your more likely to spot or hear things.
Strength doesn't, perhaps surprisingly, have any effect on damage beyond making you better with weapons that use strength. It doesn't have anything to do with how much you can carry either. Your maximum carrying capacity is based on your weight, while the penalty you get for carrying things depends on endurance.