Through Learning Torah we elevate our g-dly soul closer to g-d.
Through keeping the Mitzvos we fulfill our purpose of bringing g-d into our animal soul, into our body and into our part of the world. Through keeping the 365 negative commandments we refrain from connecting to impurity and through keeping the 248 positive commandments we bring G-D into ourself and into our part of the world.
Through all of the Jews collectively keeping the mitzvos and bringing g-d into themselves and the entire world, that will bring the coming of Moshiach.