"Come to me, all you who are weary and burdened, and I will give you rest."
These words are spoken by Jesus. Just before them, he is praising God for hiding things (I'm not sure what) from the wise and revealing them to children, and he also says that he is the one who can reveal God to people.
Just after these words, he invites us to take his yoke upon ourselves and learn from his gentle and humble heart. He again promises rest, and says that his yoke is easy, and his burden is light.
The thing that struck me most when I was memorizing this was the first three words "Come to me". There may be something there about him expecting that even though we are weak, we yet have enough power to "Come to him," but I find it more profound that he is inviting us at all.
His hand is extended to us. The door for us to come to him is open, because he has opened it.
All of us are weary. All of us have burdens that weigh us down. I found it very meaningful to simply pray through this verse, saying I want to come to you, Jesus, I am weary of this and that, I do feel crushed under burdens too heavy for me to carry, and I long for rest, I believe that you can give it to me, and I accept rest from your hand.