The term "ontology" isn't well-understood by lay people. Part of the confusion stems from its similarity to another term dealing with classification, the better-known "taxonomy". (There is a great primer document on the differences between ontology, taxonomy and classification available online.)

The word "ontology" is derived from Greek words meaning "the study of being or existance". Personally, I find it helps to think of ontology as the "science of thing-ness". So ontology asks the questions: What is this? What is that? And (critically) how does this relate to that?

More formally, one commonly accepted definition of an ontology is:

“An ontology is an agreed (and formal) description of shared concepts in some domain which has the objective of enabling shared understanding and communication...”[Zwegers et al. 2001].

Most ontologies are constructed in the form of a computer specification (see R3, RDF, Notation3) which can then be used to analyse concepts and form relationships between them. Ontologies are a fundamental part of Tim Berners-Lee's vision for the Semantic Web.

However, ontologies do not require a computer implementation. Indeed, it is my belief that English-based non-exhaustive ontologies can still prove very valuable in specifying technical meanings of terms in a domain. I plan to attempt to generate a formal ontological structure for the terms of knowledge, information and data in the near future.

UPDATE: It's worth looking at this very interesting presentation and this diagram on the overlapping uses of ontologies and an attempt to at least agree on a valid continuum.