There are several things implied here, but one is the fact that it is through opposites that we have the power to dispel evil. And what do I mean by that? Well, too often in life when trying to overcome a bad habit or repent of a sin we focus on what we don't want to happen. For example, when trying to lose weight we say to ourselves, "Don't eat." But that only puts the mental picture of eating in our heads. The mind can't imagine don't. The mind can only imagine do. A friend once told me never to say to a new teenage driver as she backs out of the driveway, "Don't hit the mailbox" because as soon as you say it, the picture of hitting the mailbox is in her head and the next thing you know a dented car hovers over a fallen mailbox while you try to console the hysterical child.
These opposities, the negatives and the positives of life, are powerful. But the most important thing to realize is that the positives have power over the negatives. When we learn to think in positives, act in positives, and deal with others in positives we bring about righteousness and avoid much pain and suffering in life. "Drive straight out the driveway!" is a positive that avoids the mental picture of hitting the mailbox. "I eat healthy," helps a dieter stay on track. Affirmative thinking is powerful.
But there is more. The only way to overcome negatives is to replace them with positives. The only way to make darkness go away is to replace it with light. It does no good to fight the dark or even say, "Go away dark." Instead you simply let in the light. Opposition can bring about righteousness if instead of fighting against the negatives of life, we ignore them, identify their opposite, and fill our lives with the positives.
The statement that there is opposition in all things means that for every bad thing there is something good. Look for it! Dwell on it! Enjoy!