You can get stronger by neural adaptation. That is, your body can recruit a higher percentage of muscle fibers in a given muscle or muscle group, it can better coordinate contraction among various muscles in the body, the firing rate of the motor units can be increased, there is decreased co-contraction, etc. This improves strength at all repetition ranges, but the effect is most pronounced at higher intensities. This involves no increase in muscle mass, but may better facilitate increases in hypertrophy due to the fact that you will able to accomplish more work, subject the muscle to greater levels of tension, and more effectively recruit a given muscle.
As well, there is myofibrillar hypertrophy. This is where there is an increase in the size of the contractile element of the muscle. This should also theoretically lead to improvements at pretty much any repetition range. The effect will be most noticeable at, once again, higher intensities.
There is also sarcoplasmic hypertrophy. This is an increase in the volume of fluid in a muscle cell. Along with this, you may see an increase in energy substrate storage (More glycogen) and possibly the enzyme levels and concentrations in a given muscle. This isn't going to help you out too much with maximal/near-maximal attempts. This will, however, provide additional fuel when working with a moderate to lighter intensity.