Those are tick marks. They're often used to denote feet (in measurement, not those things at the ends of your legs) or time. They also serve as sort of a generic apostrophe and typically in web browsers this is how an apostrophe will appear.
Proper curly quotes and apostrophes can look weird in unexpected ways in a web browser because of cross-platform issues. PCs and Macs have slightly different character sets, though since Macs now run on top of a Unix framework, there's not usually any issues of this sort between those platforms (Linux included). Also, word processing and page layout programs on a Mac will usually recognize the context and automatically put in curly quotes when it's appropriate, so the [ ' ] key is all you usually need.
And by the way, [ ` ] is not an apostrophe... it's a grave accent used in composite characters. When it leans the opposite way [ ' ] it's called an acute accent (and is also, properly, used to denote feet while this [ Ë ] (not sure what this one's called... probably something like a venti latté) is properly used to denote inches. Notice that none of these characters curl, so they're not quotation marks or apostrophes, though with some fonts there is no curl to those marks.
Confused yet?
Finally, due to the platform issues I mentioned, you may not be seeing the same marks on your PC that I typed on my Mac, while someone on a Mac most likely will unless they're using a font that doesn't include those marks.
