This passage of Scripture gives an excellent three point study for any preacher or Bible teacher to present to their congregation or study group. I noticed this some time ago and wish to share what I saw.
First, Paul says, "...God Himself has taught you to love one another." Simply put, they knew they should love other believers. This is the hallmark of a true believer.
Second, Paul goes on to say, "...Indeed, you already show your love for all the believers..." Again, simply put, they were already practicing that love for each other. The "proof of the pudding" is the practice of what one says they believe. Paul was really encouraging these believers with this point.
Third, Paul then concludes, "...we urge you to love them even more." They were being urged to keep at this with even more intensity. When you begin to really love someone you don't want your love to stagnate. You want it to grow even stronger.
These same steps could be applied to many instructions in Scripture: Know the Instruction; Practice What You Know; Improve on Your Practice. Don't settle for just knowledge. That's like saying you believe something but don't show it in your works. Don't settle for just following the instruction once. God expects a continuation of obedience. And, don't be mediocre in your obedience. Improve your skills at obeying God's Word.