The search phrase are the words typed into a Google, Bing, or other search engine. Search phrases are not always typed though, more and more often they are spoken. Spoken search phrases tend to be longer and in more natural language than typed search phrases.
The search phrase you select when using the Fertile Content tool should be one you want your content to be returned for in search results.
“Long-tail” search terms are generally those using three or more words to describe the query. Long-tail search terms are often easier to rank for. For example a search for “marbles” would be a much more difficult search term to rank high in Google for compared to “large red glass marbles”.