What is an analysis pattern?

An analysis pattern is a software pattern not related to a language or implementation problem, but to a business domain, such as accounting or health care. For example, in health care, the patient visit activity would be subject to a number of patterns.

There is a good overview from an OOPSLA '96 presentation at http://www.jeffsutherland.org/oopsla96/fowler.html

A good text would be:
Martin Fowler's Martin Analysis Patterns : Reusable Object Models, ISBN: 0201895420, published by Addison-Wesley.

In summary, analysis patterns are useful for discovering and capturing business processes.