A lot of web software converts ASCII single- and double-quote characters into special, non-ASCII open and close versions. These are sometimes referred to as "smart quotes". Their less intelligent ASCII equivalents are "dumb quotes". Smart quotes undoubtedly look better.
Here is an example.
"Some text" becomes “Some text”.
Very pretty, no? There is no smart quote key on your keyboard, so in order to make them, your software will convert them automagically. I say "automagically" because they are often converted incorrectly. There are no simple rules to convert them correctly.
I used to upgrade my dumb quotes to smart, but a couple of years ago I decided against it. Although I would like to have prettier quotes, they annoy me on other people’s sites, even when they are correctly chosen.
Specifically, they break copy-paste. When you copy text with smart quotes (and smart apostrophes, smart dashes, and other smart characters), you get crap in your text. I like copy-paste and I do not want it broken on my site. In fact, I would love it if the world stopped using smart quotes.