A common objection to Christianity is that people just don't think a good God could ever send anyone to Hell. The way unbelievers say it, you'd think God actually wants to throw many people into Hell just because it makes Him happy. But the truth is, it doesn't. Hell is not something God designed for man (and He even tells us as much in Matthew 25:41), but rather it is designed for Satan and His angels. God, by His very nature, cannot look upon sin (Habakkuk 3:13). Unfortunately, that includes us. We sin, and thus while Hell was designed for Satan, we become like Satan.
We all deserve Hell, but God doesn't want to send us there. In His infinite love, God hates punishing us, and really doesn't want us to go to Hell (Ezekiel 18:23; 33:11; 2 Peter 3:9). But He's still got to punish sin. He can't just ignore it. Thankfully for us, He has options. He can punish the sinner, or He can accept a worthy substitution. Of course, only one of those has ever existed: Jesus. Jesus, being fully God, fully man and perfectly free from sin, is the perfect candidate to take the full wrath of God on our behalf.
And He did.
2,000 years ago, Jesus became a man and lived a sin-free life. At the end of the appointed time, Jesus died a martyr on a cross, taking the punishment for every sin we have ever committed. The Bible actually says He became sin (2 Corinthians 5:21), which means that now, God can justify forgetting all our sin. No more Hell.
But it doesn't stop there. It could have, but it didn't. Not only does God not desire to punish us for our sins, but He also desires to give us eternal life. On the third day, Jesus rose from the dead, and in so doing, He earned us the right to become children of God, just through belief. Just as Jesus rose from the dead, so also can we go to Heaven when our Earthly lives are over.
There is, of course, one catch to all of this. It's not, as some say, to be a good person. You're not a good person, and on this planet, you never will be. Good works are a result of being saved, not a condition. The condition is faith. You have to believe all of this. Romans 10:9 says "if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved."
Hell is a consequence of sin. Heaven is a free gift from God. If you think Hell is an abhorrent concept, good. You're right! It is abhorrent. It is abhorrent that a human being, made in the image of God, would spend eternity separated from Him. It is so abhorrent that God Himself would go so far as to die to bail us out. Don't go to Hell. Come to Heaven.