The 'Sermon on the Mount' was a declaration of the principles of Jesus' teaching and the Christian faith.  Jesus spoke to his disciples and a large crowd on the side of a mountain, and he talked about morals and ethics, and used parables to explain some of his teachings.  He also gave specific instructions to his disciples and the church. 
"The Beatitudes" are at the beginning of this important sermon. At the time, what Jesus said was pretty shocking because each statement seemed to be the exact opposite of the values in the society of the day.  Jesus talked about people that were looked down upon  and said that they were blessed. He said that when your earthly situation is difficult or sad, God is with you to help you make good decisions and His presence is the blessing.
People are used to hearing and saying the Beatitudes as they were originally translated in the Bible (Remember, Jesus and his disciples didn't speak English!), You will find that traditional translation on the "In the Bible" page. This translation,  might make it easier for you to understand:

• God is with those who know that they need him. The kingdom of heaven is for them.
•  God is with those who are sad. They will have comfort.
•  God is with those who quietly trust Him and do not try to get their own way. The world will belong to them.
•  God is with those who are hungry and thirsty for what is right and good. They will be filled.
•  God is with those who are kind. He will be kind to them.
•  God is with those who have clean hearts. They will see God.
•  God is with those who make peace between people. They will be called God's children.
•  God is with those who get into trouble for doing what is right. The kingdom of heaven is for them.
•  God is with you when people say wrong things and lie about you, and cause trouble for you because of your faith in Him.
• Be happy and glad because heaven is a wonderful place, and God will welcome you in the same way He has welcomed the prophets you read about in the Bible.

Today the Beatitudes don't seem very controversial.  We are used to hearing them. However, it is important to think about each one and what it says about how Jesus wants us to act and how God will help us live our lives.