If you have a crush on a guy who likes your best friend, it can be very depressing to listen to him extol your friend's virtues, while you just nod and smile. If you extol something, you praise it very highly.
The Bible says: "Now I, Nebuchadnezzar, praise and extol and honor the King of heaven..." Nebuchadnezzar II was king of the second Babylonian Empire, the one who sent the Jews into exile. In some translations of the Bible, the word honor is replaced with glorify. Praise, extol, honor, glorify all mean about the same. The Bible often uses five words when one would be enough.