A ring counter is a type of shift register where the output of the last flip-flop is connected back to the input of the first flip-flop, creating a circular shift of bits. When a clock signal is applied, the single '1' bit circulates from one stage to the next in a continuous loop. Ring counters are commonly used as frequency dividers and to generate quadrature signals with multiple phases. Their applications include data counting, pattern detection, and producing square waves for timing signals.