The cash conversion rate (or simply cash conversion) measures the proportion of profits that are converted to cash flow. It is therefore:
cashflow ÷profits
This can be measured at several levels, but the profit and cash flow measures should match for this to be meaningful. One useful combination is post tax profit and free cash flow before dividends as they both measure profits available to share holders. One could also look at the conversion of operating profit into operating cashflow.
Cash conversion is important because a high cash conversion proves that profits are being turned into cashflow, and it is ultimately cashflow that matters to investors.
Conversion to free cash flow is of particular significance, when available, because it tells you how much of the profit attributable to shareholders (the measure on which valuation ratios such as PE are based) is turned into cash that could be paid to investors without damaging the business.