What does it mean that Jesus died for our sins?

When Jesus willingly gave himself up to be crucified he was obediently following the will of his God and his Father.

When he died he became a sin-offering sacrifice for sin, a sin-offering acceptable to his God and his Father Yehovah.

As a result of what Jesus has done as a sin-offering sacrifice, all of mankind has been reconciled to God, and all those who receive and live by the message that Jesus preached will be the ones who take advantage of being reconciled to God.

If they go on to be totally committed to obeying him and are baptized; they enter into water walking into their death to self, and therefore before God's Court of Justice are pronounced not guilty of their sins and therefore in His anointed one Jesus are considered to be righteous because of the power of the spirit of Jesus indwelling them.

Therefore at baptism one becomes regenerate but that is only the beginning of what needs to take place in the life of a newly baptized person because after regeneration there must be renewed, and a striving for perfection which is to become more Christlike in all one says and does.

What does it mean for Jesus to die for our sins?

Well, it introduces us to the opportunity to become new creations in him, and with his spirit and the spirit of Yehovah indwelling us we become individually a temple of Yehovah and are considered sons/daughters of Yehovah, members of the body of the Messiah Jesus, members of the congregation of God, sons, and daughters of the household of God and as grafted into the olive tree [Israel] to become a part of the spiritual Israel of God, having a circumcision of the heart as a part of the commonwealth of Israel.

Amazing Grace. We have all this from the hand of Yehovah as a result of the death and shed blood of the lord Jesus IF we accept him as our lord and King [Messiah]. And not only that, but with all of that, we have the hope of being a part of the Theocratic Government that Jesus is going to be the head of at Zion when he comes back to rule over Israel and the nations as King of kings and Lord of lords. We will co-inherit and co-rule with him during his 1,000-year rule. Praise Yehovah!