How does the red shift of distant galaxies indicate that the universe is expanding?
It is like Doppler shift of sound,
When the object is moving away the weaves gets stretched.
When the space between Galaxies is stretched out the waves get also stretched .this is red shift.
The fact that most of the galaxies show a red shift shows that the galaxies are moving away from us. If most of the galaxies are moving away this shows that the universe is expanding.
The fact that the universe is expanding implies that the universe had a beginning. This was the kernel that led to the development of the Big Bang Theory. If the universe is expanding outward it must have been closer together at an earlier point of time.