Cash flows are what ultimately matter to investors — how much money actually comes in, and when it comes in, are more important to investors than accounting profits. Profits have value insofar as they can ultimately be turned into cash.
This does not mean that cash flow is a better measure than profit, just that it is an important one. Accounting profits are calculated the way they are for good reasons. Cash flows are much more subject to fluctuations, for example because of changes in working capital. These are often the effects of timing, or one-off effects which obscure the underlying trends.
There are a number of different definitions of cash flow. Some are shown on the cash flow statement. Others need to be calculated from it, or from other accounting statements.
Free cash flow is often used as a basis for DCF valuations. Operating cash flow is used as a measure of how good a company is at converting profits into cash-flow. EBITDA is closely related to operating cash flow and is often used as a cash flow measure