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Google images, «Better half» Click to watch «Better Half» by Keith Urban

Meaning:

Your better half is your couple. Your beloved husband, wife or whatever it is. If we consider that a couple is made up by two. Your best complement is your better half.

Google images, «Better half» Click to watch «Better Half of me» by Dash Berlin

Origin:

If we cut several fruits into two and then we mixed them and then tried to put them back together again, we would realize that this task could take a little long. Since not all of the fruits are of the same size or shape, only those who could best complete the other is the better half. In the 16th and 17th centuries puritans said that each person was made up of two halves: body and soul, each one being the best half of the other. Extending this concept to a marriage, Sir Philip Sidney, a writer said that the best half was the best possible spouse.

Google images, «Better Half» Click to watch «My Better Half short story»

Example:

Google images, «Better Half» Click to watch, «Better Half» by Ginuwine