Analysis is the process of breaking down thing(s) into parts/pieces/smaller organizable units, with the goal of learning what the parts do and how they interrelate to one another.
Analysis can be defined in a myriad of ways, each differing on what is being observed and the desired end goals of said observation(s).
BusinessDictionary's preferred definitions (below) provide a solid foundation for analysis and its usage here on Open Data SE.
1. A systematic examination and evaluation of data or information, by breaking it into its component parts to uncover their interrelationships. Opposite of synthesis.
2. An examination of data and facts to uncover and understand cause-effect relationships, thus providing basis for problem solving and decision making. NOTE: this list is far from conclusive and is not even attempting to be as much.
Wiktionary's Definition of Analysis touches on the wide range of possible definitions for its use, which all fall under the context of Open Data:
analysis: (countable and uncountable, plural analyses)
(countable) Decomposition into components in order to study (a complex thing, concept, theory etc.).
(countable) The result of such a process.
(uncountable, mathematics) The mathematical study of functions, sequences, series, limits, derivatives and integrals.
(countable, logic) Proof by deduction from known truths.
(countable, chemistry) The process of breaking down a substance into its constituent parts, or the result of this process.
(uncountable, music) The analytical study of melodies, harmonies, sequences, repetitions, variations, quotations, juxtapositions, and surprises.
(countable, psychology) Psychoanalysis.