Indexes track markets in different ways, and Weighted Average Market Capitalization is a method which gives market cap, or the cumulative value of outstanding shares for a company, greater weight.
Market Capitalization is the sum total value of all outstanding shares and is one way to judge the size of a company or at least its size in the market. Indexes such as the S&P 500 are Cap-Weighted indexes, which means they give greater emphasis the to the largest companies, and the dramatic price movements of only a few of the largest companies would mean that the index would swing disproportionately for large-cap companies.
The Dow Jones Industrial Average is one of the few that does not use Weighted Average Market Capitalization, but instead uses Price Weighting, and that index fluctuates more when a security with a higher price fluctuates. Companies can have a lower price per share, but more outstanding shares (float) and so a higher market cap.