I'm intrigued by the fact that at the same time period historians believe Islam was founded and replaced Byzantium in the Middle East (7th century AD), Jews were engaged in a military struggle against that same empire. In addition both the Arabs and Jews were Semitic peoples and worshiped the same deity. Is it possible any of that is more than coincidence?
Certainly there was an important role ascribed to them in the traditional narrative of Muhammad's career and the early history of Islam. There's been a number of questions cast on the veracity of said early narrative and you can find them all over this subreddit, but I'll tell you what the traditional story is with and explain where it comes from, with the caveat that the hadiths have been questioned quite a bit lately.
There are a number of traditions about Muhammad's life of varying degrees of believability that were passed down orally and collected into collections called the Hadith centuries later, and for a long time they were all works about Muhammad would really look at, given that the Quran is only really given any serious meaning when put into the context of Muhammad's life story. Many Western scholars now, starting with Patricia Crone, call into question the believability of the Hadiths entirely, and others have stepped somewhat back from that but don't think they should be taken at face value, but at the end of the day, they're the only narrative story we have, for now.
With all those caveats in place, Muhammad's traditional story is told in a number of widely available books, Tamim Ansary's Destiny Disrupted and Karen Armstrong's Muhammad: A Biography are two that come to mind.
When Muhammad started preaching his message and it faced difficulty penetrating much beyond his immediate circle in Mecca, he assumed that the other "Peoples of the Book" would welcome him. After all, was he not, in his mind, preaching a continuation of the prophetic tradition of the Jews and Christians? Early Muhammad assumed that the Jews, especially, would welcome his message, and prayed facing Jerusalem and placed Moses as a prominent figure among the previous prophets.
This changed when Muhammad reached Yathrib (Medina), a settlement with a pre-existing Jewish population that mocked and rejected the Arab prophet, saying that the age of prophecy had ended and challenging Muhammad's knowledge of scripture. This initial rivalry turned violent when the Jews of Medina allied with Muhammad's worst enemies, the pagans of Mecca, against Muhammad's Muslims. In a brutal month-long battle, the Battle of the Trench, Muhammad's Muslims warred with the Jewish tribes of Medina, beat them, and expelled them from Medina. Muhammad ordered that Muslims would now pray facing Mecca, not Jerusalem, and reinforced that his prophecy had superseded the covenants God had made with the Jews or Christians.
Indeed, some of the Suras (chapters) in the Quaran written at later dates are pretty vehemently anti-Jewish. Sura 2 (the Quaran is ordered longest to shortest, not chronologically, Sura 2 was one of the later ones written), among other things, makes the claim that apes are the descendants of Sabbath-breaking Jews.
How much of this traditional narrative is true? It's hard to say. What is not hard to say is that up until the 1970s it was universally accepted as part of Muhammad's career and still is by many people.