In physics we have to keep tabs on objects as they move around. That is, we need to know their respective positions at a given time. In order to do this it is common to set up a coordinate system, in which we say a given point in space is labeled as zero, and all other points in space are specified in relation to that special point. An object's position then just specifies its location with respect to that special point.
If we know an object's position at two points in time we can start talking about displacement. An object's displacement is just the vector that indicates an object has moved from one position to another. Since distance is a measure of length, the straight-line distance between the two point is the magnitude of this displacement vector.