Geometry is a basis of understanding the physical world. Euclidean geometry is a basic form of geometry. If you look around, you will notice how there are all kinds of shapes and sizes. This study consisted of measuring angles, segments, points and shapes by comparison. Euclidean geometry is the study of flat space. A more recent pair of geometries, spherical and hyperbolic geometry (collectively known as non-Euclidian geometry) studies geometry on spherical and saddle shaped surfaces.
Euclidean geometry includes the ancient Greek's basic understanding of size, segments, and shapes. Axiom 2 fails to always hold on a sphere (antipodal points) and axiom 5 fails to hold on a curved surface in general. The rest of Euclidean geometry's axioms are true non-conditionally though.