This is sometimes called the "Sermon on the Plain", contrasting it with the sermon on the mount. Many people had come to Jesus, both to hear Him teach and to be healed of their diseases. Evil spirits were also cast out, and everyone wanted to touch Jesus. Power was flowing from Christ, and this was power to heal. People knew who was the source of the power.
Jesus then gives a list of beatitudes, which are very similar to those in Matthew, but with a less explicitly spiritual emphasis than in Matthew. For instance, instead of saying "poor in spirit", it simply says "poor". The key point is that there is an overturning of the natural order of things. The kingdom of God is at hand and this makes things different, it makes us different. Our natural circumstances may leave a lot to be desired, may even be very dire, but when the Kingdom comes everything changes.
There is also blessing for those who are hated or persecuted. We live in a time when our society is increasingly anti-Christian. We do not yet suffer the violence that Christians in some parts of the world suffer, but our society is ever more anti-Christian. So we need to remember these verses.
Those who seem to do well by societies measures should watch out. Now this is not a message saying riches are bad, they are not. But we need to judge our lives by kingdom standards and to seek God's riches, not worldly riches.