This is one of those verses that intrigues me, yet mystifies me. What does this mean?
"Vindicated" translates the Greek word dikaiouo. It is a legal term. It can mean "to declare guiltless." That is what you want to hear when you go to court, right? "Not guilty."
The word translated "deeds" is ergon and it means "offspring," "results," or "consequences." It refers to the results of an action. Our English word "ergonomics" comes from this word. Ergonomics is the scientific study of workplace efficiency. The purpose of this research is to help increase efficiency and productivity in industry.
Sometimes the wisdom of an act is not immediately apparent. Perhaps there are times when, initially, it appears that our decisions, or the consequent actions of our decisions, are actually foolish. But eventually they are proven to be right.
The source of this wisdom is God. The wisdom of God was embodied in the Lord Jesus. This wisdom is available to Believers by the Holy Spirit who lives in us. As Christians we should submit ourselves to the Holy Spirit. When we do He provides us with an insight that is beyond our natural cognitive abilities. And, as mentioned above, there are times when this wisdom runs counter to the conventional wisdom of our culture. At first this wisdom may appear to be acting foolishly. There may be external pressures to change your mind, to turn around, to change your course of action. But if you know that God has led you to this decision then you must "stick to your guns." There may then be a period time when the consequences of your actions appear to prove them right and prove you wrong. But all things are not as they appear to be. Eventually your actions will be vindicated.
Jesus came under attack for His methods. He associated with sinners. But He knew what He had come to do. He did not change His methods because He knew He was doing God's will, and that eventually His actions would be justified--which they have been.
Being vindicated must NOT be our motivation! Our motive must be to do God's will. When our "wisdom is vindicated by her deeds" we must not gloat. But, that being said, it is always better to be proven to be wise than to be proven a fool.