Space time curvature suggests that the the space is curved with the time. nobody will understand it without any explanation. did u ever imagine why the sky appears to be in semicircle as u know that space is abounded. also the sun doesnt go straight east-west and not in a straight line with frame of refrence of the observer on earth.
imagine i am going in space in a rocket at certain altitude i let a beam of light travel in straight line but from observer on earth the beam appears to be travelling in a curved path. but as per einstein light travels in a straight line only and in any case curvature of light is impossible. this indicates that the space is curved and along with it the time that passes with the space.
It cant be called illusion as it is the reality in the fact of space-time curvature!! another example for this can be said as light from planets. This is Einstein's special relativity. this also implies that
the time is different for different observers. the time is curved.. This principle makes the sky semicircle and the concept of horizon and travelling of moon and sun actually photons from their reflecting surface to earth