Can you give examples of such evils he described?
This is not so much a historical question as a moral philosophy or theology question, particularly since you have asked what Thomas Aquinas meant. Basically, by punishing evil, Aquinas means responding to aggression.
His thought on "just war," which basically just ties together some concepts set forth by Augustine of Hippo centuries earlier, is set out in Summa Theologica Part II-II, Question 40, Article 1. Aquinas says a war can only be just if these three conditions are met:
Your question concerns the second element, just cause, which Aquinas says has a punitive aspect. In explaining this element, Aquinas quotes Augustine on what conduct by a state would merit the punishment of war: "refusing to make amends for the wrongs inflicted by its subject, or to restore what it has seized unjustly." So those are the examples Aquinas provides.