Since your string is still a string, and not an element on the page, you could either match the angle bracket with a regex, or use jQuery to create an element and extract the source
RegExp
var content = '<span id="valuespan">This is the value of a text box</span>';
var text = content.match(/>(.*)<\/span>/)[1];
$(target-checkbox).val(text);
jQuery
var content = '<span id="valuespan">This is the value of a text box</span>';
var text = $(content).text();
$(target-checkbox).val(text);
Regular expressions suck and should be avoided if at all possible, but this is also a horrible use of jQuery. You should probably look farther back in the information chain if possible, and deal with the text another way.
edit for comment: for multiple spans, with unique IDs
var content = '<span id="valuespan1">This is the value of a text box</span><span id="valuespan2">This is the value of a text box</span>';
var fragment = $('<div />').html(content);
var text1 = fragment.find('#valuespan1').text();
var text2 = fragment.find('#valuespan2').text();