This chapter contains further discussion of risk, as defined in the previous chapter. Risk is divided into two components: systematic risk (this is the volatility of the market as a whole, since stocks tend to move in concert to some extent) and unsystematic risk (this is the volatility of individual stocks unrelated to market factors).
The theory asserts that unsystematic risk can be diversified away, while systematic risk cannot. Therefore, investors will only be rewarded for the systematic risk they take (since unsystematic risk can be diversified away). As such, high importance is placed on systematic risk, which is measured using the Greek letter beta. A stock's beta is its volatility relative to the market. The higher the beta, the higher the risk, and therefore, the higher the reward, according to Modern Portfolio Theory.
In the second half of the chapter, Malkiel discusses beta's usefulness when taken out of the academic world and applied to the stock market. He quotes studies (including his own) that demonstrate that there is no relationship between a stock's beta and it's return! However, Malkiel still believes in volatility as a risk measure. But he attributes the apparent uselessness of applying beta with the fact that it is very difficult to measure.
Finally, Malkiel argues that since higher beta does not result in higher returns, beta is still useful in that it can allow investors to find low-beta stocks and generate similar returns to the market without the volatility.