Cash Flow describes the amount of money that is actually flowing into the company or, if negative, out of the company. So it somewhat resembles the profit of the company. The difference between cash flow and profit is, while profit also takes features into account like "asset depreciation" or reserves that negatively influence the profit, those values are not covered under the cash flow. That is because cash flow only looks at transactions in which cash is actually used. Imagine you have bought an aircraft for $100 million 1 year ago. Back then it was worth $100 million of course. But now, 1 year later, it has lost some of its value because of deterioration or abrasion. So it might only be worth now $95 million. So it has lost $5 million of its former value. This has an influence on your company's profit, since your assets lose value. But it does not have any influence on the company's cash flow, because you don't "pay" these $5 million to anyone. It's just lost value, so the "cash" is untouched.
Equity Ratio measures how much your company is indebted. It is calculated as your company's equity devided by the sum of your company's equity plus your debt. So if your company is worth $100 million and you have no bank loans, then your equity ratio is $100 million devided by ($100 million + $0 debt) which is 1, so 100%. If you have a bank loan of $20 million, then it would be $100 million divided by ($100 million + $20 million debt) which is 0.8333, which means your equity ratio would be 83.3%.
P/E Ratio is in its long form "price-earnings ratio". That is a measure to see how good a stock creates value. It is calculated as current stock value divided by earnings per share of last period. The p/e ratio shows you if a stock is over- or undervalued at the stock market. If a stock is overvalued then a stock's current value might be the result of an investment bubble, because the company's profits are too low to justify such a high market price.
In real life, investors use about these values to look at a stock's value:
0 -10: undervaluation, which means that a strong growth of stock value can be expected.
10-17: fair market value for most company's
17-25: slight overvalue, or the last profit of the company was exeptionally high, or a strong groth can be expected from this company
25 +: either very high probability that this company will produce astronomically high growth rates in the future or it indicates a strong overvaluation, so a speculative bubble
Return on Equity describes how much profit your equity generates. It is calculated as profit divided by equity. It shows how much value $1 of equity generates in one period. So for example your company is only worth $1 and after one period you have a profit of $1, then your return on equity would be 100%, because $1 of equity has generated $1 of profit. If your company is worth $10 ad your profit after one period is still $1, then each dollar of your company has generated 10 cents of profit. Accordingly the return on equity would be 10% ($1 profit divided by $10 of equity = 10%).
I hope my explanations have made things a little clearer here. ;)