In the sentence you provided, "that of" serves a comparative function, helping to clarify the comparison being made. Let's break down the sentence to understand how it works: "China's social development is lagging behind that of its economy." In this sentence, "that of" is used to refer back to the concept mentioned just before, which is "China's economy." It's a way of avoiding repetition by using a pronoun ("that") to refer to a previously mentioned noun ("economy"). The sentence could be rephrased without the use of "that of" as follows: "Yet, an obvious fact is that China's social development is lagging behind China's economy." However, this version of the sentence becomes somewhat redundant because "China's economy" is repeated. To make the sentence more concise and elegant, "that of" is used to refer back to "China's economy" without restating it explicitly. So, "that of" functions as a way to indicate the specific aspect (in this case, the economy) to which the comparison is being made (China's social development compared to its economy). This kind of construction is common in formal writing and helps make the sentence clearer and more efficient by avoiding repetition while maintaining the intended meaning.

The writer is employing a relative pronoun to avoid repetition by using "that" to avoid saying "development" a second time.

"That" refers to "development". How do I know that? The clue is that "that" must refer to a noun because "that" is a pronoun, and pronouns always refer to nouns. (That's why they're called "pro"-"nouns"). There is only one noun in the sentence that "that" could possibly refer to: "development". It clearly doesn't refer to China because "China's" is only used as a modifier for "development". It clearly doesn't refer to "fact" for logical reasons and also because "fact" is far away in the sentence. So the sentence says "China's social development is lagging behind its economic development".