The bell curve
One die is flat: every face is as likely as the next. Add a third die and the totals pile up in the middle. A 10 or an 11 comes up one roll in four, while a 3 or an 18 turns up once in 216 rolls each.
Old-school ability scores
Before "roll four, drop the lowest" took over, characters were made with 3d6 in order: Strength, then Dexterity, and on down the list, no swapping. It makes heroes who look like ordinary people, which was the point. The modern method has its own roller.
Rolling under your skill
GURPS and other roll-under games use 3d6 against a skill number, and the curve makes every point count most in the middle:
| Skill | Chance to roll it or under |
|---|---|
| 10 | 50.0% |
| 12 | 74.1% |
| 14 | 90.7% |
In D&D
3d6 is the damage of a 3rd-level Sneak Attack, and it is a common roll for monster damage. The d6 page covers where else the six-sider shows up.