Since ds is frame independent we can interpret this result geometrically by treating points in the four dimensional spacetime, with ds representing the four dimensional distance [ interval ] between neighboring points.
The expression for ds looks Euclidian if the time component is taken to be ict, :
The line element allows one to classify spacetime intervals into three different classes: Consider a curve [ world- line of a particle, say] and an interval on that curve. If:
the curve is timelike in that interval;
the curve is spacelike in that interval; and
the curve is null in that interval.
Note that the sign of is a matter of convention, invariance between frames is what is important.