You can think of a remote line as an extension cord for your tank. This allows you to play without your propellant tank directly attached to your marker, so you can keep it in a harness or backpack. This also has the benefit of making your gun lighter on the field, which will aid your reflexes and mobility, and works with both CO2 and HPA.
See below for Remote Line Features & Tips.
The coiling on most remote lines keeps the line as snug to the player as possible, so it stays out of your way, while still giving flexibility so it doesn't hold you back.
Since a fair amount of players use their tank to brace their shots, you might find it more comfortable when using a remote line to add a stock to your marker.
Remote coils can be especially helpful for players using CO2, because they allow you to store your tank upright, which will prevent CO2 from spill out of the tank and into your gun.
Remote lines can have some variations. The most basic versions are essentially just a tube connecting the tank to the marker, but many coils come with extras that make the remote even more functional.