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From OALD, entrench is defined as:

to establish something very firmly so that it is very difficult to change

Does establish here means to cause to be accepted or recognized?

Edit: I came across the word from this passage:

Some people feel that this term is a bit negative, given the association with hunting and death, and they prefer more positive twists on the saying. Several organizations have even sponsored contests to come up with a new and more animal-friendly version of “to kill two birds with one stone.” However, the idea has become so entrenched in many societies that it is unlikely to fade from usage anytime soon, negative or not.

Note I'm trying to understand the meaning of establish in the definition of entrench and not a clarification of the meaning of entrench.

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closed as off-topic by RegDwigнt Aug 2 '13 at 21:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

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up vote 2 down vote accepted

I would use this definition of established from Merriam-Webster:

to bring into existence [source]

By saying the idea is entrenched the author is saying that the idiom to kill two birds with one stone is widely understood in many societies, which implies the idiom is widely used.

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Firmly rooted or ingrained. Basically that the idea has been set in place for so long that it's not likely to change.

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