To protect or overprotect a boy/girlfried in fear that he/she might find interest in someone else. Another way of cuffing is announcing a relationship loudly around a large crowd rather verbally or physically. Think of it as a relationship leash, or handcuffs (thats what it is originated from anyway)
Although meaning to "make a chick your own", the term cuf can also be used as the word "cuf" with only one F to describe having sex with a girl. Cuff can be used in two different ways.
When used in a sentence where the guy talks offensively about a girl (i.e. bitch or female) the term means "to fuck".
When used in a sentence where the guy talks respectfully about a girl (i.e. girl or chick) the terms means "to date".