A Habitable Zone is a region of space where a planet can hold liquid water (i.e., surface water), which is considered a prerequisite for life as we know it.
In particular, a Circumstellar Habitable Zone (CHZ) is the zone around a star with this potential. The concept was introduced in 1953 and to some extent is now less popular than in the past. The terms Liquid Water Zone and Liquid Water Habitable Zone are also used, but other criteria may be of use such as for the size/Frequency of Stellar Flares, etc. The outer edge is basically the system's Snow Line.
Regarding the solar system, different studies suggest different boundaries, but the region from Venus to Mars is considered a rough approximation.
A Galactic Habitable Zone is a region of a Galaxy suited to life as we know it, i.e., sufficient metallicity, and an advantageous number of catastrophic events, i.e., supernovae, Gamma-Ray Bursts, etc. Some supernovae may be an advantage to the extent that they contribute to Metallicity and Star Formation.
Some have considered radiation (alpha, beta, gamma) regarding habitable zones, i.e., just a little to assist evolution through mutation but not enough to prevent development. In my mind, this may be a bit over-oriented toward the sort of life on Earth.
California-Kepler Survey (CKS)
F-Type Star (F)
GJ 1132 b
Hobby-Eberly Telescope (HET)
Vegetation Red Edge (VRE)