I actually attend a 'Jewish roots' or 'Messianic' congregation.
It's very interesting, because the people who go there are from many different denominations. I am probably more pentecostal, but there are anglicans, baptists, even a catholic priest who attends! And also of course jewish people who are still coming to grips with the whole grace / law thing.
The teaching is very focused on what does the Bible say, instead of interpretations etc. so the messages are very non-denominational and aren't anything new or contrary to what is preached in "normal" churches (haha whatever that is

). So I see it as less of a theological movement, and more of a cultural movement if that makes sense? We celebrate the traditional jewish festivals that Jesus and the early church celebrated as well. I find these festivals particularly fascinating and enjoyable because of the prophetic meaning hidden in all of them (spoiler alert - they all point to Jesus and the Holy Spirit!).
Also, understanding some of the Jewish practices and traditions helps you to understand some of the strange habits and practices in the Bible and also a lot of the parables that Jesus said. For instance why did the lady get healed by touching the hem of Jesus's garment? That's pretty interesting to look at from a Jewish perspective... Also the church in large today is not really reading or teaching from the Old Testament and generally has a large lack of understanding in this area (speaking from personal experience here). This is something that the Messianic movement focuses on correcting by having a deepened understanding of Jewish culture etc. Personally I mostly read from the NT because there is so much life in it, but I also think it is important to at least understand the OT. And there is also a lot of beauty in it, especially when looking at all the prophecies about Jesus in the OT. (Ruth and Boaz is one example - a type or metaphor for Jesus redeeming the gentile church.)
Having an understanding from this Jewish perspective, makes it not only meaningful for yourself, but it also enables you to share the gospel with Jewish people.
The whole Bible, but also the New Testament makes it very clear that God is not abandoning His Jewish people and that He is not done with them yet. We as gentiles have the privilege to 'provoke them to jealousy.' Romans 11:11 - "Again I ask: Did they stumble so as to fall beyond recovery? Not at all! Rather, because of their transgression, salvation has come to the Gentiles to make Israel envious."
Sadly I have seen a lot of people in the Messianic movement that have adopted some unhealthy beliefs (we have to become Jews ourselves, follow the law etc.) which is not good or true, but in general I see the movement as something positive! Finding our roots again which gives meaning to today! And understanding God's purposes for Israel and their future.
P.S. Some churches see God's love for Israel as: CHURCH vs. ISRAEL. And the Messianic movement is very focused on restoring that view. God doesn't love exclusively, He is love!

But there are specific prophecies for Israel and the Jewish people that do not apply to the church. And then there are specific prophecies and blessings for the church that does not include Israel.
(Not wanting to debate on here. Just thought I would shed some light on the movement since I am in it!)