The dictionary of the Académie française defines a distance as a measurable interval separating two points in space, one object from another, or one person from another or from an object; the space travelled from one place to another.
This definition matches the intuition one may have of the term, and what is taught at school: if we consider two points A and B in the plane, with respective coordinates (*xA ; yA) and (xB ; yB), the distance between them is the length of the line segment [AB*] which is expressed, in accordance with the Pythagorean theorem, as:
d(A,B)=(xBxA)2+(yByA)2.d(A, B) = \sqrt{\left( x_B - x_A \right)^2 + \left( y_B - y_A \right)^2}.
This is referred to as Euclidean distance.