I will let someone from Amazon or speak to how they actually use data from Searches. But having worked on many web strategy and analytics projects, I can at least speak to what they can learn from the search-data.
Here are some of the things that you can learn by analyzing data from search:
- Top searched products/keywords: This should be an obvious one. This can give you insights into what are your visitors most interested in. If search for a specific product/keywords is happening too often, that product may be in high demand, and you may want to make it easy for visitor by pushing the page to your website main page or on an easy to locate banner.
- Search click-through and conversion: Which of the numerous results that a search returns get the most click-throughs or results in most number of purchases? You may want to use that as a factor in deciding the order of search-results in subsequent searches.
- Search keyword refinement: How do visitors refine their keywords in subsequent searches? As an example: If you find that there are people searching for "laser colour printer" and then refining it to "laser color printer", this may be an indicator that some of your visitors use British English, and you may want to modify your search algorithm accordingly.
- Search filters/filters: What are the most popular filters and sorting methods that visitors use on your site? An analysis of this at the user-level can help you deliver a customized experiencing, and at the website level, this can help you make important business decisions.
As an example, if a user searches for shoes, then filters it by "Gender:female", and "Price: $200 and up", and then, sorts it by "Average user rating", you can deliver more upscale items as top search results for subsequent searches. If you find a number of visitors behaving this way, you may design your future product offering keeping this insight in mind.
- Null Searches: Which search results lead to zero results (or even zero relevant results indicated by user not clicking on any of the search results) Searches that lead to zero keywords on an eCommerce website is analogous to customers coming to a grocery shop-owner, and asking for a product not on the shop. If sufficient number of customers ask for the product (and the product is inline with your business), you will like to make sure that the next time somebody asks (or searches), you have the product with you.
- Top search pages: Which pages lead to most searches? These pages may need a scrutiny. These may be pages with more insights that encourages your visitor search for the desired product and finally complete a purchase, or these may be pages with insufficient information, and that is forcing the users to use search feature.
- Search keyword correlations: Which products are often searched together in the same visit? (Example: Camera and memory card) Maybe you can consider a bundled offering for the two, or remind the user about product B, when she completes the purchase of product A.
Of course, most of these won't actually be used in isolation. For example: instead of analyzing the search-keyword correlation, website owners may instead like to analyze their sales-data to know which one are actually bought together (And I believe this is what many e-Commerce sites are already doing). But combining this with search-data will definitely lead to an additional level of insight.
See question on Quora