Placing it on the ground will let you spawn there when you die. It shows on your map and prevents zombie respawn. Only the last placed one will be active.
The bedroll is an item that may be crafted using twenty Plant Fibers as shown below, or found around the map. A Bedroll makes a single spawn point at the location it was placed at; it will be your only spawn point. After the placement, its location will be highlighted on the map. It is also recommended to place a Secure Storage Chest with some basic loot nearby in case you die and lose all the items in your tool bar and/or backpack, depending on the server settings. You can alternatively use the "Spawn near Bedroll" to spawn in a location close to your spawn point (not to be confused with the "Spawn on top of Bedroll" button). Additionally, a placed Bedroll will block zombie spawns in a rectangular area of 31x31 meters from bedrock to sky. This is especially useful to "claim" a prefab so you no longer have to worry about zombies spawning in it while you are away. Though it should be noted that this only works for "your" Bedroll, not just any that exists.