Stringer
Stringer is one of the names for the horizontal boards that are used to build wood fences.
Stringers are also sometimes known as rails, and they are usually thicker and heavier duty than fence boards or pickets. This is very important, because a wood fence stringer will be carrying all the weight of the fence boards, and if they're not sturdy enough, they might sag under the weight.
They are usually screwed in place to ensure they are well attached, although there are also special brackets that can be used to attach wood fence stringers to fence posts.
Most wood fences will have two stringers per fence panel, but in some cases (often with higher fences that are heavier) a third one might be added in the center.