Basically, T4 is the precursor to T3 and is produced in larger amounts by your body. When your body senses the circulating T3 is low, it starts converting T4 to T3, which is what actually is active in your body. It's possible to have a normal T4 but low T3 if your body doesn't make that conversion efficiently. It's somewhat like a car with plenty of gas, but no spark plugs to fire it. This is most likely if you're hyperthyroid.
If you haven't checked Medline, here is their page: www.nlm.nih.gov/medlineplus/ency/article/003687.htm