Search is a domain full of its own jargon and definitions. As this may be an unfamiliar territory to many developers, what follows are some commonly used terms and what they mean.

An engine, for the purposes of Haystack, is a third-party search solution. It might be a full service (i.e. Solr) or a library to build an engine with (i.e. Whoosh)
The datastore used by the engine is called an index. Its structure can vary wildly between engines but commonly they resemble a document store. This is the source of all information in Haystack.
A document is essentially a record within the index. It usually contains at least one blob of text that serves as the primary content the engine searches and may have additional data hung off it.
A term for a collection of documents. When talking about the documents stored by the engine (rather than the technical implementation of the storage), this term is commonly used.
Within the index, each document may store extra data with the main content as a field. Also sometimes called an attribute, this usually represents metadata or extra content about the document. Haystack can use these fields for filtering and display.
A term is generally a single word (or word-like) string of characters used in a search query.
A means of determining if a word has any root words. This varies by language, but in English, this generally consists of removing plurals, an action form of the word, et cetera. For instance, in English, ‘giraffes’ would stem to ‘giraffe’. Similarly, ‘exclamation’ would stem to ‘exclaim’. This is useful for finding variants of the word that may appear in other documents.
Boost provides a means to take a term or phrase from a search query and alter the relevance of a result based on if that term is found in the result, a form of weighting. For instance, if you wanted to more heavily weight results that included the word ‘zebra’, you’d specify a boost for that term within the query.
More Like This
Incorporating techniques from information retrieval and artificial intelligence, More Like This is a technique for finding other documents within the index that closely resemble the document in question. This is useful for programmatically generating a list of similar content for a user to browse based on the current document they are viewing.

Faceting is a way to provide insight to the user into the contents of your corpus. In its simplest form, it is a set of document counts returned with results when performing a query. These counts can be used as feedback for the user, allowing the user to choose interesting aspects of their search results and “drill down” into those results.

An example might be providing a facet on an author field, providing back a list of authors and the number of documents in the index they wrote. This could be presented to the user with a link, allowing the user to click and narrow their original search to all results by that author.