To pertain is to be relevant or somehow associated with something. If you're a lawyer, you try to find evidence that will pertain to the case and eliminate anything that is not connected.
Behind the verb pertain lies the Latin verb pertinēre, which means "to be applicable" or "to hold through." If you think the rules of the road don't pertain to you, try explaining that to the state trooper when you get pulled over. Usage note: The word pertain often takes an s at the end, as in "That pertains to this matter," but loses it with a helper: “That doesn’t pertain to it.”