Boots of Strength increase weapon damage by 1.
Boots of Strength are a valuable source of damage, especially during the early game where a player is unlikely to have found powerful weaponry. They're exceptionally strong on weapon-locked characters such as Aria or Coda, who have very few options for increasing their damage. The damage upgrade is very strong with Obsidian weaponry, allowing the user to maintain respectable damage levels even after losing their groove chain.
Once the player obtains strong enough weaponry and/or additional damage boosting equipment, Boots of Strength lose quite a bit of their value, due to the relative scarcity of enemies with more than 3 HP. In these cases, Boots of Strength are usually better replaced with hazard protection boots, such as the Explorer's Boots, Lead Boots, or Winged Boots.