The small village's economy began to burgeon after the new factory was established.

burgeon 是动词，意思是"迅速生长、蓬勃发展"。这个词源自法语，原指植物快速发芽生长的状态，后来引申为事物快速发展的意思。在句中描述经济像植物生长一样快速发展的状态。