To establish something means to begin it or bring it about. If you want everyone in your family to bring you chocolate every evening, you can establish a “Chocolates for Me” policy requiring it.
Establish is related to stable through its Latin roots and has many meanings, but all have the feel of building on a stable foundation. Besides the meaning of setting a policy, establish can also mean to prove one's value. You should establish yourself in a community before you try to bring change to it. Similarly, if you like to debate controversial issues, you'd best begin with facts that have been established and are not open to question. If you have a lot of money and want to build up your community, you can establish, or found, a school or library there.