Faceted search, also known as faceted navigation or faceted browsing, is a technique that allows users to apply multiple filters to their search queries to narrow down the results. This is a prevalent feature in e-commerce sites and digital libraries, where users often need to sift through a large number of items to find what they are looking like.

Let's take an e-commerce site as an example. Suppose you're looking to buy a laptop. A basic search functionality might allow you to search for "laptop", returning thousands of results. A faceted search feature would allow you to apply multiple filters to your search, such as "brand", "price range", "screen size", and "RAM". With each filter you apply, the pool of results gets smaller, bringing you closer to finding your ideal laptop. That's the beauty of faceted search!

In terms of our search engine, categories could be seen as classes of documents which we can add manually or derive from the documents' content. For instance, a document about machine learning in finance could be assigned categories like "AI", "finance", and "machine learning". When a faceted search is performed, our engine could first perform a regular search using the search query, and then filter the results by the provided categories.

The algorithmic challenge in implementing faceted search lies in designing an efficient data structure to store and retrieve the facets. Designing such a data structure requires a good understanding of computer science concepts, particularly in data structures and algorithms. Do remember, indexing and searching facets requires additional computational resources and hence, there might be a trade-off to consider between search precision and system performance.