Hebrews 6:16

For men verily swear by the greater - That is, they appeal to God. They never swear by one who is inferior to themselves. The object of the apostle in this declaration is to show that as far as this could be done it had been by God. He could not indeed swear by one greater than himself, but he could make his promise as certain as an oath taken by people was when they solemnly appealed to him. He could appeal to his own existence and veracity, which was at any time the most solemn form of an oath, and thus put the mind to rest in regard to the hope of heaven.

And an oath for confirmation - An oath taken to confirm or establish anything.

Is to them an end of all strife - That is, when two parties are at variance, or have a cause at issue, an oath binds them to adhere to the terms of agreement concluded on, or contracting parties bind themselves by a solemn oath to adhere to the conditions of an agreement, and this puts an end to all strife. They rest satisfied when a solemn oath has been taken, and they feel assured that the agreement will be complied with. Or it may refer to cases where a man was accused of wrong before a court, and where he took a solemn oath that the thing had not been done, and his oath was admitted to be sufficient to put an end to the controversy. The general meaning is clear, that in disputes between man and man, an appeal was made to an oath, and that was allowed to settle it. The connection here is, that as far as the case would admit of, the same thing was done by God. His oath by himself made his promise firm.