A definition essay is a type of informative essay that explains the meaning of a complicated word or concept or alters—by complicating, adding to, or otherwise changing—the standard definition of a word or concept.
An analytical essay is a type of informative essay that analyzes parts of an item (text, data set, situation, etc.) and explains their meaning, purpose, or result in relation to the whole.
Analysis is the intellectual process of breaking something (a text, data set, situation, etc.) down into smaller parts for the purpose of understanding it better.