Hubble's Law

v = recession velocity in km/sec

d = distance in Mpc

H₀ = expansion rate today (Hubble Parameter)

In words:

The more distant a galaxy, the faster its recession velocity.

Interpretation

Hubble's Law demonstrates that the Universe is expanding in a systematic way:

The further away a galaxy is from us, the faster it appears to be moving away from us.
Hubble Parameter: Rate of expansion of the Universe
H₀ is the value of the Hubble Parameter today.

Comments:

Hubble's Law is empirical - based only on data in its original form.
Not an exact law.

Nature of the Expansion

General Expansion of Spacetime:

All observers in different galaxies see the same expansion around them.
No center - all observers appear to be at the center.

What is the recession velocity?

NOT motion through space...
Expansion of spacetime: galaxies carried along.

As the Universe get 2x larger, the distances between galaxies get 2x larger.

Note:

While the distances between galaxies increase over time, the sizes of the galaxies remain the same. This is because galaxies are bound together by gravitation locally, and so do not share in the global expansion of spacetime around them.