What are "smart quotes"?

Sorry if this seems like a silly question. But, as I’m writing my document, when I enclose a word or phrase in double quotes (“like this”), LT always suggests that I change it to smart quotes. See attached.

What is the difference of double quotes vs smart quotes and why should I use one over the other? I checked the LT website, but couldn’t find any information on it.

Thanks for any information.

This is described at Quotation marks in English - Wikipedia, but I agree that the message is a bit confusing. Let’s see if we can improve it.