Translation:

The actuated fins are independent control surfaces for maneuvering the vehicle on re-entry and hypersonic speeds. Actuated fins means that they are mechanically controlled (typically through electrohyrdrostatic actuators or electromechanical actuators). This contrasts with reaction control, which is the use of smaller rockets or gas discharges to control the body through momentum transfer.

The downside of reaction control thrusters is that you need a lot of fuel to be effective. However, the downside of actuated control surfaces is that at high speeds, you can encounter a phenomenon known as "control reversal." In essence, the compressibility of air causes the reverse of what you want -- you pull back on the stick to pull up, and you nose down instead. In the early days of jet-powered flight (and some claim in WWII with powerful prop-driven aircraft such as the P-38 and P-47 in dives), this was a frequent problem.

Control reversal is when the control surface changes the structural profile such that the shock profile is changed. This can lead to flow separation, which causes the reversal of control. Modern fighter jets combat this by having all-moving tails. Since the whole tail moves, the profile of the tail never changes, so the shock caused by the leading edge of the tail doesn't get altered enough to cause the reversal. There are other issues, but we'll leave those for tomorrow's lecture.

Carmack's other idea is to modify the intertial properties of the vehicle on re-entry to get a different attitude on approach. This might in principle reduce the control requirements, e.g. instead of coming in like a brick, come in like the space shuttle. But Musk claims that the size of the vehicle makes that prohibitive. In short, the long body of the Falcon magnifies the effect of offset centers of gravity. For example: grab a one-foot long piece of lumber. It's pretty easy to hold even if you don't hold it at the center. Now, grab a twelve-foot long piece of lumber. It's much more difficult to carry even if you're grip is only a few inches away from the center.

Since these four fins each have (at least) three-degrees of freedom and move independently, you effectively have twelve-degrees of control authority, which will help in ensuring that the vehicle enters a suitable state for landing.