The hem of a Jew's garment was not just a simple fold of the garment, doubled over and sewn down to prevent the edge from fraying. It was an ornamental highlight which made a statement about the rank and significance of the wearer. The removal of the fringe of a man's garment was the equivalent of removing part of his personality . To cut off the hem of a wife's garment was regarded as divorcing her. Fringes of garments were used in a similar manner to a signature or personal seal.
The hem or fringe of a garment indicated the position or individuality of the wearer. Jesus rebuked the Pharisees for enlarging the borders (fringes) of their garments.
But all their works they do for to be seen of men: they make broad their phylacteries, and enlarge the borders of their garments Matthew 23:5
The obvious deduction being that they were thereby trying to make themselves look more "important". The tassels on the fringes were formed by the threads decorating the fringe being brought together at the corners of the garment and knotted. The original purpose of the fringe and tassels as stated in the law became obscured in course of time, becoming a more of a tradition, than anything else.
In the Old Testament account, David spared Saul's life in a cave, but he took away the verification that he had him in his power:
And the men of David said unto him, Behold the day of which the LORD said unto thee, Behold, I will deliver thine enemy into thine hand, that thou mayest do to him as it shall seem good unto thee. Then David arose, and cut off the skirt of Saul's robe privily. 1 Samuel 24:4
Why did David cut off part of Saul's clothes? Why did his conscience bother him after he cut of the garment? There was special significance in the act of cutting off the hem (fringe) of Saul's clothes, which Saul was not slow to recognize.
Behold, this day thine eyes have seen how that the LORD had delivered thee to day into mine hand in the cave: and some bade me kill thee: but mine eye spared thee; and I said, I will not put forth mine hand against my lord; for he is the LORD'S anointed. 1 Samuel 24:10
David had robbed Saul of his status symbol, his "signature", "his personal seal", his rank and his significance; the fringe of Saul's robe that identified him as king.