The series of video by ScienceClic is very succinct yet clear.

First, we know in space-time full dimensions all objects travel at the same speed ||v|| = c, light speed and the unit can be defined 1. And then we need to get rid of the empirical intuitive notion built on Euclid Geometry.

Using an example of airplane traveling from west sphere to east sphere, we can easily understand the geodesic versus normal Euclid. Next, the concept of metric tensor!

Because Pythagorean theorem stop working, we apply a more generic/accurate form aided by metric tensor – math tool