The Hubble constant (H0) is the current rate of expansion of the universe, which is presumed to be constant throughout the current universe. It is expressed as a ratio of the relative velocity between two points that results from the current expansion to the current distance between the points, typically expressed in km/s divided by megaparsecs. Measurements put it in the in the range of 50-90 (km/s)/Mpc with current determinations close to 70. The zero subscript (H0) can be thought of as the lookback time (time counted backwards from the present). This expansion is termed the Hubble expansion. Hubble time is the reciprocal of the Hubble constant, a simplified calculation of the age of the universe, a useful approximation. It is the interval of time since the instant at which the universe would be a point, given expansion at the current rate.
Observation has revealed evidence that the universe's expansion is not constant with time. The term Hubble parameter (H or H(t)) is used to indicate a similar characterization of the universe's expansion without specifying we're talking about right now. Despite this variation, the Hubble constant (current value) is often used as a good approximation of the expansion for nearly the entire life of the universe.
The term Hubble parameter is also used for what could more precisely be termed the dimensionless Hubble parameter, indicated by h.
H = h × 100 km s-1Mpc-1
The currently determined Hubble constant places the current value at about 0.7. Distances to galaxies are sometimes given in terms of this Hubble parameter: e.g., a distance of 30h-1 Mpc, which allows future readers to adjust the distance they assume according to up-to-date values of the Hubble constant. Using a constant value of h = 0.7, 30h-1 Mpc calculates to roughly 43 Mpc.
The terms are named for Edwin Hubble, who in the early 20th century established that distance determinations to galaxies using variable stars correlate with radial velocity measurements of the galaxies by redshift (illustrated by his Hubble diagram), thus, with one, you can reasonably estimate the other. This is termed Hubble's law, a useful means of approximating distances to galaxies, an approximation termed the galaxy's Hubble distance (DH).