It can be broken down as follows:
~ism ....................... the philosophy of
~arian~ ................. those people who believe in
~anti~ .................... opposition to
~dis~ ...................... the removal of
~establishment~ .. the Church of England as the official state church
Antidisestablishmentarianism is often quoted as the longest English word that has an actual meaning, is not a proper noun or scientific term and was not made up on the spot to form a "longest word."