I've been writing numerous posts on exactly that for a couple of days, now.
The moniker "Hebrew Roots" is used in contradistinction to "Messianic Judaism". It is actually a shortening of the original, "Hebrew Roots of the Christian Faith".
Once, HR designated a group or individual who taught about the history and culture of Israel in order to enhance Christian engagement with the Biblical text. However, in the past 10-15 years, HR has taken on a life of its own. Due to increased understanding of Biblical times, followers of HR began to identify error in their churches, and turned away from the Christian community. At the same time, these people refused to adopt the Jewish community--ironically, for the same reasons.
Thus, at this point in time, HR has come to mean Bible teaching that encourages an absolutist perspective ("Everything except me is pagan!"), leading to judgmentalism and disdain for the established religious communities of Judaism and Christianity.
One of the doctrinal positions that goes with the package is Two House teaching, which allows Gentiles to entertain the fantasy that they are "true Israel" (despite the fact that there is almost always zero evidence of any Israeli blood).