Dynamics is the way of describing the relative levels within a piece of music. Thus - Dynamics processors are used to correct or control signal levels. The most famous dynamic processor is a Compressor.
A compressor provides a form of automatic level control. It attenuates high levels, thus effectively reducing the dynamic range, making it much easier to control signals and set appropriate fader levels. Reducing the dynamic range also means that recording levels can be set higher, therefore improving the signal-to-noise performance. Limiting is an extreme form of compression, where the output signal is sharply attenuated so that it cannot exceed a particular level.