Most scholars study philosophy by analyzing the famous works of historical philosophers. They analyze these works by developing an interpretation. Philosophical interpretation may refer to a lot of things, but, in general, it refers to an analysis and understanding of the core concepts or meaning of something. For example, one scholar might interpret Heidegger's views in "Being and Time" as an exploration of authenticity, while another scholar might call it a rumination on the process of "being." Both of these are interpretations, or accounts, of Heidegger's primary points in his work.
Interpretation is not restricted to mere summary. It also uses the theories of other philosophers and events in history to contextualize an argument. For example, a person may attempt to understand the writings of Soren Kierkegaard within a Danish Christian theological context. In other words, a person might see how Kierkegaard's ideas stem from other ideas in his environment and respond to certain historical events in his personal history. This is a broad interpretation.
Interpretation may also look for a particular topic or perspective within a piece of writing. This is called hermeneutics, which is a method of interpretation. Hermeneutics might regard gender relations, social hierarchies, economics, race relations or any other preoccupation within a piece of writing. For example, one could analyze Wittgenstein's views of faith in his writings on logic. Although faith might not be his primary topic, one can use references to faith as a method for interpretation.
Interpretations in philosophy are often subject to debate and change, which is why they are interpretations and not facts. Facts would be immutable ideas that are indisputably true. Interpretations represent a person or group's perspective on something, which may be subject to change. Re-interpretation refers to the process by which a person or group explores something for a second time and develops a new or changed idea of that thing.