The Hubble constant (H0) characterizes the rate of expansion of the universe. Hubble's law (aka the Hubble law) is a theory that the universe is expanding such that the velocity at which an object is moving away from another is proportional to the distance between them, i.e.,
v = cd
where v is velocity, d is distance, and constant c is H0, the Hubble constant. Estimates are in the range of 50-90 (km/s)/Mpc with current estimates very close to 70. This expansion is called the Hubble expansion.
A Hubble diagram is a diagram mapping redshift to known distances to objects (e.g., galaxies), so a straight line demonstrates Hubble's law and the slope indicates Hubble's constant.
Observation has revealed evidence that the universe's expansion is not constant. One might say "the Hubble constant changes with time", but for much work, this issue can (or must) be set aside, and even when it is relevant, the term Hubble constant is often used specifically to mean the current rate of expansion.
The Hubble parameter (h) is a dimensionless variant on the constant, where
H0 = h × 100 km s-1Mpc-1
h calculates to 0.7. Distances to galaxies are sometimes given in terms of the Hubble parameter: e.g., a distance 30h-1Mpc, which allows future readers to adjust the distance they assume according to up-to-date values of the Hubble constant (i.e., for H0 of 70, that distance would be roughly 43Mpc).
The term Hubble flow is used for the apparent motion of astronomical objects due to this expansion.
The term Hubble time indicates the period of time since the universe was a point, assuming the expansion was constant at the current rate. Since determining the current rate is non-trivial, the Hubble time is subject to refinement. Other factors, including variation in the expansion rate are taken into account to produce a more accurate estimate of the age of the universe. Current estimates of Hubble time and the age of the universe differ by on the order of a percent. Timescales of processes are compared with the current Hubble time to see whether any instance of the process is likely to have completed, or equivalently, whether some observed phenomena might be the result of an instance of the process.
The terms are named for Edwin Hubble, who in the early 20th century established that galaxies are more-distant Milky Way-like objects, and later that the distant ones can be seen to be receding from us, suggesting an expanding universe.