An analysis layer is something that uses the results of middle-layer calculations to display or visualize data or to do some kind of an analysis. 

The ice-d.org web server is an analysis layer. It displays exposure ages for a particular site or sample. 

GIS software could be an analysis layer that displays exposure ages on a map. 

Some kind of a paleoclimate reconstruction based on the exposure ages of glacial moraines could be an analysis layer. 

An analysis layer typically uses both raw data from the data layer and also derived results from the middle layer. Like, the paleoclimate analysis example probably wants to know the location and elevation of glacial moraines as well as their ages.