This is one of the Cherry Hill recommendations that did not get implemented the first time around. For an example of what this might look like, see this mockup (especially the "Search Terms in Context" sections): http://cherryhill.github.io/aspace_pui/design-elements/phase1_final/SearchResults_landing_final.jpg
For a real-world example, see https://sova.si.edu/search?q=carrot . Here, I've searched for the term carrot in SOVA. Notice that if the search term is found at a lower-level of description (as this one often is), then you get those deep search matches within the search result, which includes links and highlighting. (sidenote: this model from the SOVA search could also be used to achieve the Cherry Hill recommendation to enable users to group their results by collection).
In working toward this, we need to make sure the relevant fields are indexed and stored rather than just indexed.
Since implementing the PUI we’ve had a number of people asking for this.
The example Mark Custer provided above also batches multiple results from a single record, which is something I’ve gotten requests for in order to lessen the overwhelm of thousands of results at the archival object level. This can also make more apparent which resource records contain the most relevant hits.