Nor shall you swear by your head, because you cannot make one hair white or black. For whatever is more than these is from the evil one. Initially, the emphasis seems to be on the prohibition of swearing. However, a little reflection reveals that the real focus is keeping one's word.
Words are powerful.
As the spoken word of God brought creation into being, and as Jesus spoke the words of the Father and kept them, so our speech should reflect a similar power and integrity. In the Old Testament economy it was not at all unusual for people to swear oaths. Many of the faithful heroes swore such oaths. You shall fear the LORD your God and serve Him, and shall take oaths in His name. He was a murderer from the beginning, and does not stand in the truth, because there is no truth in him.