The term "backronym" is used to refer to a number of things. Most commonly, it means an acronym which is made by deciding on an acronym and then devising a name or title to fit it. The USA PATRIOT Act is one such example; lawmakers wanted to the name of a groundbreaking piece of legislation to turn into a memorable and distinctive acronym, so they created the desired acronym (i.e., "USA patriot") and then fit the name to it (i.e., "Uniting and Strengthening America by Providing Appropriate Tools Required to Intercept and Obstruct Terrorism"). Backronym also refers to a word which seems like an acronym, but actually isn't.
An acronym is a pronounceable word which is made out of the first letters of a phrase or organization. Some acronyms fudge it, leaving out words like "a" and "the," or including the first two letters of some words for flow. You can probably think of a number of familiar acronyms; radar, for example, which stands for Radio Detection and Ranging, and NASA, which comes from National Aeronautics and Space Administration. In some cases, organizations decide on a backronym to make themselves memorable; the National Organization for Women, for example, undoubtedly liked the thought of being referred to as "NOW," so they may have chosen their name around the desired acronym.
In the case of words which look like acronyms but aren't, there are a number of different types of acronyms. The term "DVD," for example, is actually an initialism (or alphabetism), where each letter stands for a different word, but each letter in the initialism is read individually, not together as a word. A pure acronym is a word which might feel like an acronym, but isn't, as in the case of "wiki," which is Hawaiian for "quick." It is also possible to see replacement acronyms, created when a company wants to change its name, but keep its branding.
Making up a backronym can be an enjoyable activity, and some people like fitting new acronyms to existing words or company names, usually in an uncomplimentary way. Many people create backronyms in a satirical way; The Health Institute of Nutrition (THIN), for example, is actually a spoof organization created by fat activists, with a name which was designed deliberately to turn into a funny and ironic acronym.
The creation of a backronym can also be an important consideration when a company establishes itself, as the name of a company or organization can have a huge influence on its success. Many companies convene boards to discuss potential names and the acronyms that they might turn into, and in some cases a company may create a specific backronym to send a particular message or to create a product association in the minds of consumers.