Inner meaning of this statement is that we need to "remove our attention", remove our sense of self, our attention to ourselves.
The coming of Moshiach in an individual's service of Hashem is stopping to be associated with my personality, with my animal soul, and to meet, greet, and receive my Neshama. This is how Tzadikim lived, and now it's available to each and every one of us.
Come out of my exiled mentality, my habitual existence, my habits. There is no more power to the anuimal soul to control and hide my G-dly soul, only when I am used to experiencing life through my personality, then by my habitual behavior I add more vitality in my animal soul and this is what is now concealing my G-dly soul.
When we exit our habitual consciousness and meet our neshama, we become G-dly beings, like we were meant to be, this is receiving Moshiach on an individual level. This is also what it means to do Teshuva, since Teshuva is "and the soul shall return to the G-d that created it" as is explained in Tanya. This is why "they do Teshuva and immediately are redeemed".
To experience how Ronnie the soul is seeing Ronnie the person behaving in the physical material world. Sweetening (hamtaka).
To experience our G-dly soul, not our animal soul. To get used to it. This is Chukas - burning the desires and will of the material personality and thus G-dliness is revealed, in me, my life, and the world.