This model is part of the Objectory method created by Ivar Jacobson. It is basically what the system would look like if it were a fluffy cloud constructed entirely out of idealised objects. It ignores non-functional constraints like language, distribution and persistence. Those are captured in the Design Model.
The Analysis Model really comes into its own in large scale, distributed systems. Understanding how such things work is a daunting task if you have to get your head around all the design artefacts that have been put in to cope with things like resilience and scalability. The Analysis Model presents a simplified view that all developers can understand. This is important if the integrity of the system is to be maintained; without it, it is too easy for developers to tinker about in the design and break functionality.
-- Mike Howells
See original on c2.com 