Resolve is a measurement of Jin Sakai's strength as a samurai. Jin can spend resolves to recover his health or perform special combat techniques. Jin can gain resolve by parrying attacks and killing enemies.
Find your resolve and fight through the pain.
― Lord Shimura
Resolve was first introduced in the Prologue as part of Jin's training flashback with Lord Shimura. As what Lord Shimura said, Jin doesn't actually heal, he actually fights through the pain and his injuries will gradually heal in the lore.
In the beginning, you can collect up to 3 resolves. Progressing through the game and completing bamboo strikes will increase the resolve you can have at any one time, the maximum possible number of resolves is 10.