A black box is a device used to provide visual representation of a subject's memories. The subject, generally an unconscious person nearing death who is no longer capable of relaying their memories verbally, is first provided a neuro-stimulant to improve mental clarity. This allows a conscious person to interact with them and request that they recall certain events.
Only one black box was ever depicted in Travelers - when Rick Hall was near-death after being attacked by Faction agents, the core team used a box designed by Grace Day to ascertain the identity of his shooter. It is assumed that medical nanites do not interfere with the process, as Hall had been treated with these as well. (Philip)