Fence

Fences were added in the Secret Friday update 8. They count as one and a half blocks tall and so cannot be jumped from the same level. They occupy the centre of blocks automatically connect to one another and can be stacked. Fences can be placed on top of both kinds of pressure plates. Also, you will find that if you put other blocks on top of it the fence will only count as 1 block high. In Survival Multiplayer, if you stand on a fence, the server will count it as an illegal move, and begin to "rubber-band" you back and forth, allowing little to no movement.

Stacking
You can stack multiple fences on top of each other. To do this you need to use a simple block like sand and place it where you want to have 2 layers. After you've placed the block, place the Fence on top of the block and remove the block below. If done correctly, the Fence will be floating and you can place another one underneath.

See picture below for a visual explanation.