A W-shaped recession begins like a V-shaped recession but then ends up turning back down again after showing false signs of recovery. W-shaped recessions are also called "double-dip recessions" because the economy drops twice before a full recovery is achieved..
A W-shaped recession is painful because many investors who jump back into the markets after they believe the economy has found a bottom end up getting burned twice---once on the way down and then once again after the false recovery.
The recession of 1980 that double dipped in 1981 and 1982 is a great example of a W-shaped recession.
Check out this video describing W-Shaped recessions to learn more.