Here's a simple explanation:
All items, when used enough naturally increase in tiers. Unlimited items (upon reaching tier .9, 1.9, 2.9, etc) may manually be "tiered up" to the next tier integer by using a bunch of materials (it tells you when you right click the item and click "tier upgrade"). If you do not tier them up to the next whole number, they stop gaining tier growth.
(L) items automatically advance in tiers (even through the whole numbers).
Socket components and all those other odd things (like Surface Hardeners and Focus Lenses) are used to create enhancers which are then popped into the opened slots on your item.
Blazar fragments are used as a material for tiering up unlimited items, and Nova fragments are used in the manufacturing of enhancers.
A word of warning:
When you attempt to tier up an unlimited item, you must have a duplicate of the item you wish to tier. If your Tier Upgrader profession level is not high enough, you have a chance of failing the tiering, and possibly run the risk of losing your second item as well (it's not fun, trust me).
Enhancers, when fitted to an item, generally raise the amount of decay when the item's used. On weapons it also increases the amount of ammunition used per shot. For this reason, the ammunition in-game was multiplied by 100 to create more nuances in the amounts of ammunition. Basically, 1 PEC buys 100 units of ammo, but an Opalo now takes 200 medium cells to shoot.
There are also tier growth rates on all items. I'm honestly not totally sure how they work. Seems to be that higher numbers are better and let your items tier faster, so higher numbers are good for (L) items.
I think that's about it. Tiering can be very expensive and EXTREMELY risky. Hell, I just did my first successful one today (GDC).
Good luck out there.