Standard Reinforcement is a basic form of improving weapons and armor in Dark Souls II, that also appeared in Dark Souls beforehand. It is independent of the other Infusions unlike in Dark Souls; you can reinforce an infused weapon, and a reinforced base weapon will not lose its levels from infusion. Also, in constract to Dark Souls, common equipment can be reinforced only up to +10, not +15.
Weapons that upgrade with Titanite Shards improve damage characteristics by 10% per upgrade. Scaling values will increase gradually and, in some cases, move up a rank (i.e. going from A to S). This basic upgrading may be performed 9 times, before needing a Titanite Slab. Once this process is completed, your weapon will be twice as effective on top of any scaling bonuses it gained.
To reinforce, the player needs an item that is able to be reinforced, the required Titanite and sufficient Souls. For regular titanite weapons, one will need to use 6 Titanite Shards, 6 Large Titanite Shards, 6 Titanite Chunks, and 1 Titanite Slab to ascend a weapon to +10. This can be done through Blacksmith Lenigrast, Steady Hand McDuff, and Weaponsmith Ornifex, however you cannot do it yourself in the fields and labyrinths of Drangleic.