In a perimeter-weighted iron, for example, weight is redistributed to outer areas of the clubhead - around the perimeter, in other words. This is accomplished by "scooping" out a portion of the construction materials from the rear of the clubhead, creating what is called a "cavity back." Removing material from that area allows more material to be added around the perimeter, changing the weighting properties.
Why do this? Perimeter weighting causes changes to a club's center of gravity location, its moment of inertia (resistance to twisting on off-center strikes), the amount of flex in the clubface, its feel and even sound at impact. Add it all up, and perimeter-weighted irons offer significantly more forgiveness (basically, they are easier to hit) than irons that are not perimeter weighted.
Karsten Solheim, the founder of Ping Golf, is credited with introducing perimeter weighting to golf clubs, his first clubs designed with perimeter weighting going on the market in the late 1960s. Prior to that, all irons were musclebacks, which do not have cavities behind the clubface, are less forgiving and more difficult to hit well.
For more, see this FAQ: Why does perimeter weighting make an iron more forgiving?