Establish is a verb with multiple meanings:
1. To set up (an organization, system, or set of rules) on a firm or permanent basis
2. To achieve permanent acceptance or recognition for
3. To show (something) to be true or certain by determining the facts
4. To introduce (a character, fact, etc.) into a narrative
5. To settle (someone) in a new place of residence or way of life
Establish这个词儿可有意思了，咱们来掰扯掰扯：
1. 最常见的意思就是"建立、设立"，比如开公司、定规矩啥的。举个栗子："咱得establish个新部门"就是说"得成立个新部门"
2. 还有"确立、使被接受"的意思。比如说："这牌子establish了自己的市场地位"就是"这牌子站稳了脚跟"
3. 法律上常用，意思是"证实、确定"。比如："律师establish了不在场证明"就是"律师证明了不在场"
4. 写作时指"引入、交代"。比如说："小说开头establish了主角背景"就是"小说开头交代了主角背景"
5. 还有个不太常用的意思，指"安顿、安置"。比如："他在新城市establish了自己"就是"他在新城市安顿下来了"
补充说明：商务场合establish特常用，特别是谈合作的时候，老外总说"let's establish a partnership"，其实就是"咱们建立个合作关系"的意思。