"With the rapid development of the society and economy" can be expressed as "As the society and economy rapidly develop."

The phrase comes from the observation that as society and economy progress, they tend to grow and change at a rapid pace.

Examples in Engpsh:

As the society and economy rapidly develop, new technologies are emerging at an unprecedented rate.
The rapid development of the society and economy has led to significant improvements in people's standard of pving.

Examples in Chinese:

随着社会经济的快速发展，新技术正以前所未有的速度出现。
社会经济的快速发展已导致人们生活水平的显著提高。