Enzymes and Reversibility of Reactions
I think Feynman is referring to the second law of thermodynamics.

The entire statement is this:


  The most important feature of the cycle of Fig. 3–1 is the transformation from GDP to GTP (guanosine-di-phosphate to guanosine-tri-phosphate) because the one substance has much more energy in it than the other. Just as there is a “box” in certain enzymes for carrying hydrogen atoms around, there are special energy-carrying “boxes” which involve the triphosphate group. So, GTP has more energy than GDP and if the cycle is going one way, we are producing molecules which have extra energy and which can go drive some other cycle which requires energy, for example the contraction of muscle. The muscle will not contract unless there is GTP. We can take muscle fiber, put it in water, and add GTP, and the fibers contract, changing GTP to GDP if the right enzymes are present. So the real system is in the GDP-GTP transformation; in the dark the GTP which has been stored up during the day is used to run the whole cycle around the other way. An enzyme, you see, does not care in which direction the reaction goes, for if it did it would violate one of the laws of physics.


Now, there are some mistakes here. For instance, GTP is not used in the muscle contraction but ATP. Perhaps this was not quite known during Feynman's times. Coming to the point, I think what Feynman means is that external work has to be done by the enzyme (that catalyses the GTP-GTP exchange) if it is actually moving the chemical equilibrium towards one side (against what would happen in an uncatalyzed condition). Some enzymes can actually do that (shift equilibria and catalyse one sided reactions), by using energy from ATP hydrolysis or other energetic transformations but since they are performing work by using energy from an external source, they are also not violating the second law.

That's the essence of the second law of thermodynamics: you cannot move heat from a cold reservoir to a hot reservoir unless external work is done. We don't have "heat" here but there concept is the same for chemical energy and reaction rates.