What is an assurance case?
Assurance Cases are the more generalized form of Safety Cases, an approach used in the Safety community to convey what was done when creating a system to ensure that it would act safely under a wide variety of scenarios. Assurance Cases can be used to document a Safety Case but they also can convey any other critical behaviors the system should exhibit during its operation. These critical behaviors are documented as "Claims" about the system - it is secure, it is safe, it is reliable, it weighs 3 pounds, it uses less than 1 watt per hour, etc.
These claims are then sub-divided into sub-claims, iteratively, until you have a sub-claim that can be shown to be met with some type of evidence. Think of a tree of claims, sub-claims, and more sub-claims capped off with evidence that you argue shows that the sub-claim is met. The other important part is to make explicit the assumptions and prerequisites of the system design/implementation. All systems have bounding/foundational assumptions about heat, humidity, types of inputs, and other items - with an Assurance Case these are captured explicitly and used as a consistency match between that system and the one it is part of, in that if the encapsulating system does not honor or support the assumptions and prerequisites of the enclosed system then the claims about that system's behavior will be invalid since the assumptions used to engineer the system may be undermined. There is also a standard from the OMG - the Structured Assurance MetaModel (SACM) that defines how to exchange Assurance Cases - providing a way to compose Assurance Cases for the sub-systems of a system and as long as assumptions and prerequisites are met - for composing those systems and their claimed capabilities. See:
Introduction of Assurance Case Method and its Application in Regulatory Science - FDA hosted article
Assurance Case - Science Direct Articles
A Short Introduction to Assurance Cases - University of York