The lift supports on a vehicle can be either in the front or rear and their function is to reduce the effort needed and to stabilize the opening of a trunk or hood. The most common type of failure for these parts is a loss of gas pressure inside the tube due to permeation, high temperatures, or frequency of use. When this occurs, the hatch or hood will fail to stay in the open position, or it will be more difficult to lift or open. If these parts aren't replaced immediately, it won't usually cause a failure of the hood or trunk to open, but it will make it more difficult. Without the lift supports, the hood or trunk would close much harder than intended and cause damage to the latch or body panels surrounding the edge of the hood or trunk.
A lift support has two major components: a rod and a tube. The rod slides into and out of the tube and on the end of the rod inside the tube are valves. The valves provide the pressure and resistance as well as holding in the "spring" energy that's used when the hood or trunk is opened. These lift struts are gas-charged with some viscous fluid in them to provide resistance. On either end are attaching points in different styles depending on the vehicle. Many are ball-and-socket types, some are bushings with a bolt, and there are a few others out there. They vary in length depending on the manufacturer. Most of them are application specific, so you'd need to find out the exact part numbers that would fit your vehicle.
The installation for lift supports is relatively easy. The following are instructions for uninstalling and installing the lift struts for most vehicles.