Modeling Processes with Process Composer 
SAP NetWeaver Business Process Management (BPM) enables you to model, connect, compile, deploy and maintain composite business processes.
A process model is an abstraction of a process and describes all the aspects of the process:
Activities: steps that are executed within the process
Roles: users or systems that execute the activities
Artifacts: objects, such as business documents, for example, that are processed by the process
The process composer is the design time of BPM where you create the process models.

The process composer is integrated into SAP NetWeaver Developer Studio as a separate perspective and provides BPMN (Business Process Modeling Notation) based process modeling capabilities. BPMN is based on the specification adopted by OMG (Object Management Group). This notation allows easy and intuitive process modeling both for business analyst type of users and developers in one common environment. The process composer supports all stages of process modeling from high-level definitions of the process down to the enrichment for the actual development into deployment and execution. Life cycle aspects (versioning, transport and so on) are fully supported through SAP NetWeaver Composition Environment. SAP’s BPM notation differentiates activities into human and automated activities. Those activities can be structured within nested processes (subprocesses). Human activities trigger tasks, which are executed through end users, whereas automated activities allow Web services to be executed and therefore provide full integration into SAP’s enterprise SOA enabled business applications.
More information about the SAP's BPM notation: Using BPMN Process Models
The process desk represents the human interaction management part in BPM. It provides a centralized process and task management. The business users can centrally access and execute their tasks and can additionally display their tasks in a process context.
More information:Managing Processes and Tasks with the Process Desk.
The process server represents the runtime services in BPM. The integration into the SAP NetWeaver Administrator enables you to start and stop processes, to monitor and manage processes and tasks, and also to troubleshoot processes.
More information: Monitoring Processes with the SAP NetWeaver Administrator