Restrictive is an adjective that describes something that keeps people within certain boundaries. A household where you aren't allowed to play video-games, watch TV, or eat junk food is restrictive.
If you noticed that restrictive is wrapped around the word strict, you're on to something. Strict comes from the Latin stringere, and you can probably guess what that means, right? Well, not "string," actually, but close: "to bind tight," either with string or rope or whatever does the job. The kids in a restrictive household are kept from doing so many things they might as well be tied up.