Glow berry farming is the process of producing more glow berries by bonemealing an existing one, or by leaving it and harvesting it when it increases in height. It allows you to obtain more glow berries without having to find them. Glow berries are extremely rare outside bonemealing or growing them, with the only other way having to find them in mineshaft chests, so having a way to farm them is handy, however the primary use of glow berries is for decoration (they make a good aesthetic light for most builds, especially rustic style) since it can only be used elsewhere to breed foxes and a very low saturation food, so consider that before deciding to produce more of them.
Manual farming is quite straightforward. You can use the mechanic that allows you to produce more by bonemealing, or you wait for it to grow and then harvest it. The first method requires you to have some bonemeal and at least one glow berry. Just place a glow berry and keep right clicking or tapping on the berry while holding bonemeal, which will make it produce a glow berry in its bushes, then when you tap on it again it will eject the berry which you can then pick up. The second method is basically like an upside down bamboo farm. Just wait for the glow berry to grow and then harvest it using shears or silk touch.