There are two major factors in the selection of an investment--risk and return. The capital asset pricing model (CAPM) is a method which attempts to describe the relationship between these two factors. CAPM introduces the concept of the risk premium. If someone were to pay a certain amount for a risk free investment, the risk premium prices in the premium an investor is willing to pay for x amount of added risk for the required return.
The assumptions are not realistic, but that does not really matter (I believe). The fact that they are not realistic does not affect the concept or practice of using the CAPM. For example, no investor has an unlimited amount of access to borrow or lend funds at a risk-free rate, nor do all investors have the same time frame or expectations. However, if we were to attempt putting these parameters on the model (taxes, borrowing limitations, various time horizons, and the like) it would make our calculations so complex and convoluted that they would become useless. Having said that, the CAPM certainly still has its critics who claim that making all of these assumptions skews the results.
The CAPM can be very useful in designing an optimum bucket of investments to maximize return. It assumes two types of risk: systematic and unsystematic. While the model cannot diversify away systematic risk (inflation, economic turmoil, geopolitical events, and the like), it arguably can diversify away a good portion of unsystematic risk (which is related to the specific security, industry, etc.). It can do this--in theory--by selecting enough securities in the portfolio to reduce the beta.