Distance describes how far something has traveled, and displacement describes how far something is from where it started. Distance is often a scalar. Displacement is often used with vectors. An object's displacement can never be greater than the distance traveled.
When someone travels to the store and heads back home, the total displacement of the vehicle is zero when it parks at home. When the car is parked at the store, however, its displacement is greater than zero. The total distance traveled, on the other hand, is a positive value. Displacement deals with distance from the starting point while distance itself deals with how far it traveled.
Displacement is often used as part of a vector. Displacement combined with the time it took to get there results in a vector value for velocity. Distance traveled combined with the time transit took, on the other hand, represents speed.
These two measurements are useful in different scenarios. When calculating how many miles a trip put on a car, the total distance is most relevant. When determining how far a driver is from home, displacement is the important value. In common speech, however, displacement is rarely discussed, and people are more likely to refer to displacement as the distance from a particular point.