Dividends per share means just what it sounds like.
It's the dividends that a company pays out per share and is a commonly used per-share metric like earnings per share, free cash flow per share, or book value per share.
Although the definition of dividends per share may be relatively simple, it's an important concept in investing with a number of implications for investors, and it plays a role in several valuation models.

Cash Flow
Total dividends paid out are also included on the cash flow statement and help investors assess a company's capital allocation. However, if you're an individual shareholder and want to understand how much you're being paid from dividends, you need to be able to calculate the dividends per share.