A breakout is when the price moves through a support or resistance level and keeps moving in that direction. However, if the price moves through a support resistance level, but then fails to continue moving in that direction and instead reverses course is known called as failed breakout.
For example, assume the price of a stock has reached Rs 2000 several times in the past, but each time it is fallen after reaching it. This is a resistance level. If the price moves above Rs 2000, that is a breakout. If the price then falls back below Rs2000, and keeps dropping, that is a false breakout. The breakout lost momentum and the price reversed.
Hope this answer your question.