Within the Lift ecosystem, "contexts" can be thought of as pre-defined functionality that makes data available to the personalization tools, when that data exists in the current state (of the site/user/environment/whatever else).
The simplest use of contexts is in mapping their data to UDF fields on
/admin/config/content/personalize/acquia_lift_profiles. When the context is available, its data is assigned to a UDF field and included with Lift requests. For example, the Personalize URL Context module (part of the Personalize suite) does exactly this with query string contexts.