When you have swords that you have too many of or you want to raise some of the stats of other swords, you do this under Refine. The only stats you can refine are ATK (Attack), LEA (Leadership), MBT (Mobility) and FOR (Force). To raise RCN (Reconnaissance) or HP (Hit Points), see Duties.
When you enter Refine, you will be asked to choose the sword you want to refine. Please note that stats that are purple means the stat is maxed out and can no longer be raised. Once you choose a sword, you will then be brought to a screen where you can use up to five swords at a time materials.
In order to use a sword as refining materials they must be unlocked (can be done from formation), not assigned to any teams and must not be performing any duties. The first of a sword you receive will always be locked by default, so do not worry about accidentally using a sword that you have either one of or have leveled as refining materials.
Every sword has a cap on any bonus stats in refining in any of their forms. When you reach that cap, you will see a stat marked as MAX in purple on the screen. You may find yourself wanting to use a sword to refine another, but one of its stats will not do anything to one of the stats. This is normal. You will almost always max out MBT or FOR before any other stat as the game will always give you an abundance of Tanto.
It is generally recommended that you wait until a sword goes into Toku form at level 20 or 25 before refining a sword. This is because all the bonus stats are lost once they level up. Also, any sword that you use as refining materials will have troops and horses removed and placed back into your inventory automatically.