“Roots” refers to origins. In the phrase “Hebrew Roots” the term relates to the foundations of the Christian faith which is the faith of the Hebrews.

“Boast not against the branches. But if thou boast, thou bearest not the root, but the root thee.”
(-Romans 11:18).

“And in that day there shall be a root of Jesse, which shall stand for an ensign of the people; to it shall the Gentiles seek: and his rest shall be glorious.”
(- Isaiah 11:10).

From this angle, “Hebrew Roots” is synonymous with “Messianic Roots.”
-Teddy

Definition from a Jamaicain perspective:

Roots: The truest form of reggae music. As its name dictates, roots is the true foundation–the cornerstone of a host of musical branches. These are the traditional vintage Jamaican sounds that have almost become extinct with the invention of the computer chip. Very few bands today still play these foundational sounds as they were initially created. General market reggae artists like Culture, Burning Spear, John Brown’s Body, Midnight and Cultura Profetica still carry on this classic sound, while gospel artists such as Christafari, Solomon Jabby, The Israelites, and Leon De Judah are still holding up the torch of roots music for future generations. (Quoted from Gospelreggae.com)