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The Hubble constant (H0) is the ratio of the relative velocity between two points within the universe due to the universe's current expansion, to the current distance between the points. This is an expression of the current rate of expansion of the universe, presuming the expansion to be constant throughout the current (and recent) universe. It is typically expressed in km/s divided by megaparsecs, and measurements put it in the range of 50-90 (km/s)/Mpc with current determinations close to 70 (i.e., between 65 and 75). The zero subscript (H0) can be thought of as zero lookback time (time counted backwards from the present). This expansion of the universe is termed the Hubble expansion. Hubble time is the reciprocal of the Hubble constant, a useful approximate calculation of the age of the universe. 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 useful 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 of h at about 0.7. Distances to galaxies are sometimes given in terms of this Hubble parameter: e.g., citing a distance as 30h-1 Mpc, which allows future readers to adjust the distance they presume according to future determinations of the Hubble constant. In effect, such a distance measure is merely another means of giving the galaxy's absorption redshift. If h = 0.7 is presumed, then 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 either 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).
Of note is that determinations of the Hubble constant in recent years, which are expected to be accurate and precise, are contradicting each other: determinations using the CMB are in the range of 66-68 and those based upon the cosmic distance ladder (particularly Cepheid variables) are in the range of 72-75, for as much as 10% difference, a very large difference compared to the determinations' expected uncertainty, a discrepancy termed the Hubble tension.