By using the armor and weapons that you equip yourself with, you will generate "attachment points"* and when your attachment points reach 100% you will be able to convert them into "materia." This is known as "materia conversion." "Materia" is a crystallized form of the weapon and armor’s stats that the player has used and formed an attachment to.
The way I understand it is that once you reach 100% attachment points, which are attained by equiping gears (maybe some gears attune better together then others) you get to transform these gears into materia which is a crystalized stat augment that you attach to another gear. So you lose the orignal gears to attach to your new gear.

It doesn't just grow on your gear. And you need the help from crafters to attach it to the gear and the gatherers to provide the catalyst to attach it.