In a physical system the eigenvectors represent "modes" of random "vibration" (random movement) of a system and the eigenvalues represent the variance (i.e. amplitude) of each of these modes. The eigenvalues added together equal the variance of the overall (combined) movements (the Decomposition Property). In the stock market the main mode (biggest eigenvalue) is the common market movement (stocks' tendency to go up and down together) sometimes called the market factor or beta factor. There is no agreement on what the second is, but it might be, hypothetically, an upward movement in high book-to-market stocks on a day when the low book-to-market stocks go down. In any case, the eigenvalues 2, 3, ..., n involve some category of stock going down/up and some other category going up/down. In the 1970s it was thought that the second mode might be stocks that benefit from higher oil prices (oil companies) go up while stocks that are hurt by rising oil prices go down. Sensitivity to other macroeconomic factors were also considered as possible modes (interest rates, inflation, the USD exchange rate). Nowadays small cap vs large cap or Value vs growth are popular candidates. In any case the exact description of these factors is not easy (it probably changes over time) and is not really the objective of this type of article. They generally just try to describe how many modes would explain most (say 80 or 90%) of the variance, i.e. the "complexity" of the stock market. The main conclusion is that one mode (one eigenvalue) is not enough (therefore rejecting the CAPM as an adequate model of variance) and that there clearly other modes that are important. The size of the 2d eigenvalue compared to the first is a measure of the inadequacy of a single factor model to explain the stock market; all studies show that the second eigenvalue is clearly not negligible compared to the first.