The phrase legacy survey is incorporated into names of some astronomical surveys, such as the DECam Legacy Survey. As far as I can tell, the phrase suggests the survey aims to collect data of wide and lasting utility. Often the survey requires considerable resources and often the survey's resulting data is made freely available.
The phrase legacy survey appears to be derived from programs associated with major telescopes (such as the Archival Legacy Program for the HST) for surveys that fit the above description and are selected to receive significant observation time due to these "legacy" benefits, and often it is the names of such programs' surveys that include the phrase.
HST has other programs for surveys requiring significant resources, that have the same general program aim, but differ in details regarding requirements and selection criteria for candidate survey proposals. One such program is HST's Treasury Program and there exists at least one survey that labels itself treasury, i.e., the Panchromatic Comparative Exoplanet Treasury.