A context defines a namespace, a set of context variables. These work much the same as session or request attributes in the servlet spec. You may bind any value you like to a context variable, but usually we bind Seam component instances to context variables.
So, within a context, a component instance is identified by the context variable name (this is usually, but not always, the same as the component name). You may programatically access a named component instance in a particular scope via the Contexts class, which provides access to several thread-bound instances of the Context interface:
User user = (User) Contexts.getSessionContext().get("user");
You may also set or change the value associated with a name:
Contexts.getSessionContext().set("user", user);
Usually, however, we obtain components from a context via injection, and put component instances into a context via outjection.