Being ambidextrous means that you are able to use any hand as your main hand. Depending on the value of the trait, you can use either hand or both at the same time.
+2: You have equal dexterity and proficiency with both hands, meaning that should your "main hand" be injured or restrained, you may use your offhand without any penalty.
+4: Not only are you equally dextrous with both hands, but you possess the coordination to do two different things with each hand, which gives you a free attack action in combat, similar to if you had used Stress, but without suffering the penalty, provided that your weapons and equipment would logically allow another attack. You cannot dual wield rocket launchers or greatswords, for instance.