Legal Definition
A grace period is a defined, specified timeframe granted by a court or regulatory body to allow parties to meet certain obligations, deadlines, or requirements before the consequences of failure become immediate or punitive.
Plain-English Translation
It means a short extra amount of time given to someone to finish something or fix a problem before a strict deadline hits. For example, if you have to submit a paper by Friday, and you get an extra few days to finish it without penalty.