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.