From Wiki:
The Soft Tail (also Softail) relies on the flexing of the rear triangle and a rear shock or elastomer placed in line with the seat stays. Soft tails are a variation of the original Amp Research Mac-Strut design (technically a 3 bar suspension design). Soft tails have no moving parts, besides the shock/elastomer, making it extremely simple. It maintains pedaling efficiency and power delivery because of the solid chainstays. They tend to be extremely light compared to other rear suspension types. Soft tails are out of favor now because of the limited rear axle travel of these designs - typically around 1 inch. Some examples include the Trek STP and the Moots YBB.