If all the convertible securities a company had issued were converted at once to common stock, the stock would be diluted; Diluted EPS reveals by how much.
Companies will sometimes entice investors to buy bonds or preferred stock by giving them an option to convert them into shares of common stock. If a bond is converted, shareholders equity increases on the balance sheet and liabilities go down, since a debt liability is being retired.
But, if this occurs many times, the amount of earnings each share experiences will go down noticeably; keep in mind that even though the company saw a windfall of money by terminating a debt obligation and liquidating the reserves that backed the obligation, the cash flow and earnings are probably not going to continue to support that uptick in shareholder equity.
The diluted earnings per share is a calculation which states the hypothetical earnings per share the company would have if all of the convertible securities were converted into common stock at one time. Analysts and investors are skeptical of a company with a high diluted EPS.
Too much dilution can potentially trigger a death spiral where short sellers and additional conversions pile on a downtrend.