Antidisestablishmentarianism is one of the longest words in the English language. It is often used just because of its length, and not because of its meaning. Part of the reason for this is that antidisestablishmentarianism describes something that people no longer talk about very much.
An official state church is called the "established" church, so a disestablishmentarian is a person who wants to get rid of the established church. This person's ideas are called disestablishmentarianism.
And antidisestablishmentarianism describes groups of people who are against getting rid of the established church. It is very often used to describe those who don't want the Church of England to stop being established. In other words, they want the Church of England to continue being established.