You can use double quotes instead of single quotes:
theAnchorText = "I'm home";
Alternatively, escape the apostrophe:
theAnchorText = 'I\'m home';
The backslash tells JavaScript (this has nothing to do with jQuery, by the way) that the next character should be interpreted as "special". In this case, an apostrophe after a backslash means to use a literal apostrophe but not to end the string.
There are also other characters you can put after a backslash to indicate other special characters. For example, you can use \n
for a new line, or \t
for a tab.