Does it mean the company pays 3% of the total earnings to the stock holders? So if I have a stock that has 1$ EPS I would receive 3 cents?
It means a 3% return on the value of the stock. If a stock has a $10 share price, the dividend would be $0.30.
Normally though, the dividends are announced as a fixed amount per share, because the share price fluctuates. If a percentage were announced, then the final cost would not be known as the share priced could change radically before the dividend date.