You can use either form of quote. These are identical:
var html1 = "<bold>Hi</bold>";
var html2 = '<bold>Hi</bold>';
Whichever delimiter you choose to start the string with, the next unescaped occurrence of that delimiter signals the end of the string.
Where life gets interesting is when there are embedded quote marks in your string itself. For example, supposed you want to assign this to a javascript variable:
<img src="http://www.google.com/images/logo1w.png">
In that case, you a couple choices. You could use this which escapes the embedded double quotes:
var html1 = "<img src=\"http://www.google.com/images/logo1w.png\">";
or you can use this:
var html2 = '<img src="http://www.google.com/images/logo1w.png">';
I find that the latter looks a lot cleaner.