In the words of Freeman Tilden, the revered pioneer of natural and cultural interpretation,

Precisely what is this thing called interpretation, which is now offered so extensively not only by the  National Park Service, but also in many state parks, municipal and county areas, and city nature centers as well as in in privately administered museums and historic sites? It would be easier to state precisely what it is not. It is not instruction. It is not avowed information, though it carries information with it. It is not forced upon anyone. Take it or leave it. If one takes it, one has it in  any forms, the ideal being to make each form as attractive as possible--the guided trip, the marked trail, the campfire gathering, the slide talk, the motion picture, the exhibits and printed matter.
A somewhat clumsy but generally accepted definition in the "trade" is this: an educational activity which aims to reveal meanings and relationships through the use of original objects, by firsthand experience and by illustrative media, rather than simply to communicate factual information. If that sound stuffy, you may call it "an attempt to reveal the truths that lie behind appearances." [Freeman Tilden, "Mindsight: The Aim of Interpretation," National Parks 43, no.260 (May 1969), pp.9-12]

His seminal work on interpretation, Interpreting Our Heritage, appeared in 1957. His six principles of interpretation as coined at the time are:

1. Any interpretation that does not somehow relate what is being displayed or described to something within the personality or experience of the visitor will be sterile.
2. Information, as such, is not Interpretation. Interpretation is revelation based upon information. But they are entirely different things. However all interpretation includes information.
3. Interpretation is an art, which combines many arts, whether the materials presented are scientific, historical or architectural. Any art is in some degree teachable.
4. The chief aim of Interpretation is not instruction, but provocation.
5. Interpretation should aim to present a whole rather than a part, and must address itself to the whole man rather than any phase.
6. Interpretation addressed to children (say up to the age of twelve) should not be a dilution of the presentation to adults, but should follow a fundamentally different approach. To be at its best it will require a separate program.
[Freeman Tilden, Interpreting Our Heritage, Chapel Hill: The University of North Carolina Press, 1957]

Several years ago, the U.S.-based National Association for Interpretation came up with an updated definition of interpretation, circulated through the collaborative Definitions Project, as follows:

A mission-based communication process that forges emotional and intellectual connections between the interests of the audience and meanings inherent in the resource.