Archimate is a modelling language for Enterprise Architecture. We are adopting as the EA modelling language at the University, and it has been adopted by The Open Group which also maintains the TOGAF standard. As of version 2.0 the main language corresponds with phases B, C, D and E of the TOGAF ADM, and it has extensions that closely relate to aspects addressed in the Preliminary phase and Phase A.
Archimate represents the enterprise architecture in Business, Application and Technology layers, and in each layer there are active structure elements (capable of displaying behaviour), behaviour elements (the unit of activity performed by one or more active structure elements) and passive structure elements (on which behaviour is performed). Elements ‘connect’ to each other through relations such as association, access, used by, aggregation and composition. Elements can be put into groups, mainly for ease of conceptualising a view.
My view, and that of many others, is that Archimate should be used for the high-level view of the enterprise and, taking business processes as an example, going one or two levels deep into processes. It would not normally be used for detailed business process modelling though, with that requirement better met by a notation such as BPMN.
The full specification is available from The Open Group, but I would also suggest reading Mastering Archimate by Gerben Wierda for a good guide on practical uses of Archimate.