Wide binaries refers to binary stars that are orbiting each other, yet thousands of AU distant from each other: one criteria is "on the order of 7000 AU". They have gained interest as a possible test of gravitational models, including Newtonian gravity and general relativity (GR), along with the theory of dark matter. (Newtonian gravity and GR differ, but they converge as you go to smaller scales, a necessary condition of any theory of gravity given how clearly Newtonian gravity matches observation at scales within the solar system.)
The visible portion of galaxies and galaxy clusters do not follow these models without assuming there is matter that has not been detected (for which he term dark matter has been coined). Galaxies and galaxy clusters are the largest scale gravitationally-bound objects available for analysis to explore this. If gravity has some other pattern at large scales (i.e., varying from Newtonian and GR), then the analysis of intervening scales are of interest, such as wide binaries. Stellar clusters promise to be of similar use.
Studies have claimed that wide binaries don't fit the concept of dark matter, based upon orbital speeds that are faster than can be explained by GR/Newtonian. (Since relative velocity and these theories are often used to determine if two stars are gravitationally bound, some additional means must be used, such as changes in relative velocity over time.)
The abbreviation PHWB has been used for planet-hosting wide binaries.