The problem comes from the fact that the laws of God meant there was punishment for not obeying them. This punishment ultimately was eternal separation from God. God didn't create hell for us but rather for the fallen angels. But it just so happened that us choosing our own way would mean the law would demand us to end up in hell. It's just like the laws of the country you are currently residing in. If you steal, there is bound to be a punishment. The jails aren't constructed with you in mind but you sure would end up there if you say, steal and break the law of the land.
Now the "jail sentence", if we can use that illustration, has been served. We are no longer required to serve that sentence for the sins we have committed in the past, present, or future (no matter how great they are). This does not mean we continue in our sinful way but that God's grace exists when we do. It's like having airbags in your car for protection. You don't go about crashing the car because you have airbags but rather the airbags are there in case you do crash by accident. Now, all we have to do is believe that He has indeed come down to this earth, paid the price for our sins, died for us on the cross, rose up again by God's Spirit on the third day, and set us free from a life of bondage and slavery to sin. It says in the Bible that Jesus is now sitting at the right hand of God. He promised while He was here on earth that He will go to prepare a place for us. So we believe, as Christians, that when we die, we will be in heaven, in that amazing place that God has prepared for us all.