There are blacksmiths in each of the two cities. They can sharpen your swords to increase their damage, or add a status effect to them so they inflict negative status effects on enemies.
The blacksmith in Bavelock is Brock who owns Fire and Steel. The one in Savina is Argamir who owns Argamir's Blacksmith.
Before you can talk to Brock you must complete the sidequest "Helping Jaden". Jaden is irritated that Brock is always busy smithing on a particular sword and will not open his blacksmith to his customers, so he asks you to talk to Brock.