What does the Torah mean when it writes that 'Hashem will circumcise your hearts ... '?
Ramban: It means that when, in the time of Mashi'ach, you will do Teshuvah with all your heart, Hashem will help you to achieve your aim, 1 by cutting away the bad part of our hearts 2 so that we have no more desire to do evil - like Adam ha'Rishon before he sinned. 3
Seforno: It means that when you try to cling to Hashem with all your heart, Hashem will open your eyes to move away from all errors that confuse your minds from knowing the truth, so that you will automatically acknowledge His goodness and love Him.
Targum Yonasan: It means that when you do a complete Teshuvah with all your heart, Hashem will remove all foolishness from your hearts, because He will remove the Yeitzer ha'Ra from the world 4 and create a Yeitzer Tov which will guide you to love Him ... .
Ramban: As the Gemara says in Shabbos, 104a 'ha'Ba Letaher, Mesayin oso!' ('Someone who comes to purify himself will receive Divine Assistance').
Ramban: Like one cuts away the Orlah by a B'ris Milah.
Refer to Bereishis, 2:9:3:1.
See also Na'ar Yonasan
What will change after Hashem circumcises our hearts?
Ramban: Hashem gave man the freewill and choice to be a Tzadik or a Rasha from the creation until the time of Mashi'ach. Then it will all change, and people will have a natural tendency to do only what is good. 1
Sha'arei Teshuvah (1:1): Hashem will help penitents who still grapple with their nature, and create in them a spirit of Taharah to attain the level of loving Him. 2
Refer to 30:6:1:2-3.
Ramban: As the Pasuk states in Yirmiyah, 31:30-32. See also Pasuk 33 and in Yechezkel, 36:26, 27. See also Shabbos, 151b.
There will still be free choice, only Hashem will help those who choose correctly.
What are the connotations of the (otherwise superfluous0 words "Lema'an Chayecha'?
Seforno an Targum Yonasan: It mens 'in order that you will live forever.
