Meschiach literally means "the anointed one." It was part of the coronation of an earthly king of Israel, in those years when they had one, hence a symbol for earthly rule, not heavenly.

It is true that basic Judaism still yearns for a redeemer, yet to arrive. Even among the Reform movement (I count myself as one), the "messianic age", a.k.a. "times to come", get a mention in the weekly service.

In my own personal brand of Judaism, I take the entire thing as symbolism: "A better world awaits." Hope doesn't need a singular object -- one can hope in a more general sense, for a condition, not a person. Another important core Jewish belief and action is called tikkun olam, "fixing the world". It proposes, oddly enough, that God needs help finishing creation. It means that we humans are responsible for making a better world, and not to sit around waiting.

Jesus said, "The kingdom of heaven is all around you." He was talking about tikkun olam.

The liberation of Judea from Roman rule is not the reason that convinces Jews that Jesus wasn't it. None of the prophecy about the benefits of life under the King of Kings has yet to be fulfilled; hence, we look askance at claims of partial fulfillment.

A while back, I had a revelation of sorts about why Christianity holds on to a version of the Jewish Bible while denying that their followers are not bound by the Law within it: It's simply for the prophecy, without which the writers of the Gospels could not have retroactively made their claims for Jesus. Why the early Church kept any of the books other than the Prophets is beyond me...

My usual book recommendation: The Five Gospels.