To redouble means to greatly increase your effort or intensity, especially after an initial attempt hasn't succeeded. When you redouble your efforts to master long division after struggling on the first few problems, you buckle down with serious determination, committing yourself much more fully than before. A basketball team might redouble their defensive efforts after giving up too many points in the first half.

If you were already working hard and you redouble your efforts, you're now working much harder than before. A scientist might redouble her research efforts after a promising early result, or a detective might redouble his investigation when new evidence appears.

Redouble often appears in situations where the stakes are high or time is running out. It suggests committing yourself with renewed focus and energy, pushing yourself significantly harder than you were before. When a teacher says the class needs to redouble its preparation before the state assessment, she means everyone should dramatically step up their studying.