It means that the laws of physics are the same everywhere and the same in every direction. It is of fundamental importance as these symmetries give rise to conservation laws. The isotropy of the universe means that angular momentum is conserved; its homogeneity means that momentum is conserved. A similar symmetry, that the laws of physics are the same for all time, gives us conservation of energy.

See Noether's Theorem on Wikipedia for more information.

What is meant when it is said that the universe is homogeneous and isotropic?
After she killed the Levi squad, Eren transformed to fight the Female Titan. In Chapter 29, Hammer, it looked like Eren was having the upper hand, but then the Female Titan turned around, and with one horizontal motion, cut Eren's titan form's head in half.

How did that happen? That part wasn't clear in the anime nor the manga. Did she take a tree and smacked him? Did she harden her hand and hit him?


