Price to Book Value (P/B) ratio is a measure of a firms price per share in the market (market value) to the firms Book Value per share (Accounting value of assets).
If the P/B ratio is greater then 1, then the markets (investors) value of the firm, is greater then the value of its assets. If the ratio is less then 1, then the market values the firm at less then its asset value.
Price to Earnings (P/E) ratio is measure of a firms price per share to the firms Earnings (Accounting value of profit).
If the ratio is greater then 1 then the market is valuing the firm at a multiple to its current earnings. This multiple is sometimes be used as an indicator of how much earnings a firm is expected to have over its life. If the ratio is less then 1 then the market values the firm at less than its current earnings.
It is very rare for a firm to have a P/E or a P/B of less then 1. The simplest reason for this is that the price per share of a company includes a value for the entire firm, not the book-value of assets or current earnings. No one knows all the factors that the market takes into account when it values a company. Individuals also value things differently, and the market is made up of different individuals. Hence, what may be cheap to some is expensive to others.
My thesis is very ambitiously going to try to capture some of these factors which firms may have in common given their P/E and P/B Quadrant. (eg High P/E and High P/B, Low P/E and low P/B, High P/E and Low P/B, Low P/E and High P/B).