A price movement through an identified level of support or resistance that does not have enough momentum to maintain its direction. Since the validity of the breakout (or breakdown) is compromised, many traders close their positions and the price fails to make the sharp move that many were expecting.
A failed break is also commonly referred to as a "false breakout".
As you can see from the chart above, technical traders who identified the descending triangle would expect a substantial move lower once the price was able to break below the $21.50 support. However, in the event of a failed break, the move lower would not occur and many traders would be forced to realize a significant loss. Many technical traders will use other technical indicators to confirm that the breakout is valid and that the momentum will likely continue.