Studying Torah (the Written and Oral) is the main way we attach and connect ourselves to G-d and grow spiritually. The Messianic Era is meant to be a time without any extraneous concerns in order to facilitate our ability to study Torah and accomplish this to the greatest extent possible.
In the words of Maimonides (or at least a translation of a translation of his words):
For these reasons, all Israel, [in particular,] their prophets and their Sages, have yearned for the Messianic age so they can rest from the [oppression of] the gentile kingdoms who do not allow them to occupy themselves with Torah and mitzvot properly. They will find rest and increase their knowledge in order to merit the World to Come.
And in another place:
The Sages and the prophets did not yearn for the Messianic era in order to have dominion over the entire world, to rule over the gentiles, to be exalted by the nations, or to eat, drink, and celebrate. Rather, they desired to be free to involve themselves in Torah and wisdom without any pressures or disturbances, so that they would merit the World to Come...