Capabilities are a way of expressing security, which are claimed to work better than the ubiquitous AccessControlLists (ACLs). The basic idea is reminiscent of the LawOfDemeter: you can speak only to objects you have created, or objects that you were created holding, or objects which have been passed to you.
See http://www.eros-os.org/essays/capintro.html at the ErosOs web site for a introduction to the notion of capabilities. See http://www.erights.org/elib/capability/index.html for capability computing as it is implemented in E (the EeLanguage).
See CapabilitySecurityModel, ObjectCapabilityModel, CapabilityOrientedProgramming.