You will understand it fully if we start explanation with extract request message, which performs fingerprint template extraction from fingerprint images placed in applicant element in extract request.
Extract request has response_content element and you define there what are you interested in (what you are expecting in the response message). For example you set there that you want fingerprints template, their quality and format in which the response fingerprints template should be returned.
Identify and verify requests contain applicant (like extract request) and on Eafis3 extraction is performed as well (in case fingerprint images are present in applicant) - before identification or verification can be done. So you are able to request that not only identification or verification result is what you are interested in but also extracted template and fingerprint qualities (like in extract request). For example to decide how relevant is the identify result based on returned quality score of fingerprint images (provided in identify request applicant).