It's the dwelling place of God the Father
Matthew 6:9 (NIV)
“This, then, is how you should pray:
“‘Our Father in heaven,
hallowed be your name
It's a place of treasures that thieves can't steal.
Matthew 6:20 (NIV)
But store up for yourselves treasures in heaven, where moths and vermin do not destroy, and where thieves do not break in and steal.
It has many rooms
John 14:2 (NIV)
2 My Father’s house has many rooms; if that were not so, would I have told you that I am going there to prepare a place for you?
It's an actual place
John 14:2-4 (NIV)
2 My Father’s house has many rooms; if that were not so, would I have told you that I am going there to prepare a place for you? 3 And if I go and prepare a place for you, I will come back and take you to be with me that you also may be where I am. 4 You know the way to the place where I am going.
It's being prepared for us
Compare this to the idea that it's just a "state of being". It's not. It's a place that is being prepared.
John 14:2 (NIV) supports this. Also:
Jesus said in Matthew 25:34 (NIV)
"Then the King will say to those on his right, ‘Come, you who are blessed by my Father; take your inheritance, the kingdom prepared for you since the creation of the world."
It's a place of reward
This is in the middle of a parable that Jesus was telling regarding what heaven would be like.
Matthew 25:23 (NIV)
His master replied, ‘Well done, good and faithful servant! You have been faithful with a few things; I will put you in charge of many things. Come and share your master’s happiness!’
There won't be a need for marriage in heaven
Luke 20:34-36 (NIV)
34 Jesus replied, “The people of this age marry and are given in marriage. 35 But those who are considered worthy of taking part in the age to come and in the resurrection from the dead will neither marry nor be given in marriage, 36 and they can no longer die; for they are like the angels. They are God’s children, since they are children of the resurrection.
It is everlasting/eternal
John 3:16 (NIV)
For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.