Okay kiddo, so disestablishmentarianism is a big fancy word that means people who believe that we should separate (or "disestablish") the church from the government.
See, a long time ago, in some countries like England, the church was super powerful and the government and the church were all mixed together. This meant that the people who ran the church (like the priests and bishops) also had a lot of say in how the government ran things.
But some people didn't like that. They thought it was unfair for one group to have so much power and that everyone should be able to believe whatever they wanted without the government and church telling them what to do.
So disestablishmentarians believe that church and state should be separate, and that everyone should be free to practice their own religion (or not have one at all) without the government or church interfering.
It's kinda like when you play tag at recess - everyone gets to run around and have fun, but nobody can be in charge or make all the rules because that wouldn't be fair! Disestablishmentarianism is all about wanting the same thing for religion and government - everyone should have a fair say!