I don't have any diagrams showing the locking brummell, (there are pics on the site, but they might be missing right now). I think I can explain it...
For your splice, you passed the working end through the standing end. This formed your eye. You passed the working end through the standing end AGAIN, then buried the little tail. Taper, bury, stitch and your splice is done. Your splice is unstitched right now. You should see that if you held the rope in a certain way and pulled on 1 side of the eye, you could take that splice apart in about 3 seconds.
For a locking brummell, you start the same. Pass the running end through the standing end to form the eye. Now you pass the STANDING end through the running end. Taper, bury, stitch and your splice is done. Except this time you'll see that this forms a "lock" where the tail CAN'T come out. More secure slightly less strong.
It's up to you which you prefer. They each have their pros and cons. The splice you have now is well done. However, don't use either without stitching that tail down!!!