A decade counter is a digital circuit that counts through ten states from 0 to 9 using flip-flops to represent binary-coded decimal values. It advances its count with each clock pulse and resets to 0 after reaching 9. Decade counters are used for applications like frequency division and timing control where large numbers of counts are needed but space or power constraints prevent larger counters. They have advantages like a large count range from a simple design and wide availability but also limitations in resolution, speed, and power consumption compared to other counter types.