Paintball remote lines make it possible to have your tank mounted in a backpack or pod pack, giving you additional mobility with your marker. One of the most common uses of remote lines is for kids who may have a difficult time holding a fully loaded marker, tank, and hopper, so by moving the tank to a pod pack, it helps to greatly reduce the weight of their setup, allowing them to play a little more comfortably. Other uses for remote lines include running large tanks for big games, pistol setups that you want to use air rather than Co2 carriages, and they are commonly used for Airsoft.
There are some different types of remote lines, including coiled, straight, with and without slide check. Coiled vs straight lined remote lines are partially up to personal preference, but coiled lines do have a higher likelihood of catching branches or debris while running through the woods while straight lined remotes have a smaller chance of that happening. Slide check is something that greatly helps degas your marker quickly so you can set it down or disassemble your set up, with it you simply slide the collar back to degas from that point forward, holding air in the line prior to that point. From there you can quickly detach your marker, whereas if you did not have a slide check, you would need to turn the air off from the tank, degassing everything in the line and marker, then you would be able to detach your marker from it once the line has bled out.