Clockwise from upper left:
Leaf shelter - can be built in jungle terrain.
Wood shelter - can be built in woods.
Lean-to - can be built anywhere from parts you carry with you.
Brush shelter - can be built in scrub terrain.
Temporary shelters can be built by the player. The lean-to is built using parts the player is carrying (wood, hide, and cordage). the others are built in specific types of terrain from readily available materials.
Temporary shelters provide shelter from precipitation, thereby reducing or eliminating the chance of damage from exposure.
They are quite small, you can build bedding in them, but that's its. All four shelters shown have bedding in them. the only actions available while in a temporary shelter are things like "rest and heal" and "sleep".
Still, a night sleeping on bedding in a dry lean-to beats a night on the hard ground in the rain with a cold chill on the air and no fire.
The game tracks the condition (quality) of all objects, and models wear and tear, weathering, breakage, and items wearing out. Pretty much any object that can be made can be inspected to determine its current condition, and can be repaired, demolished, or abandoned. Temporary shelters last about 3 game months if not maintained.