Getting the text the user has selected is relatively simple. There's no benefit to be gained by involving jQuery since you need nothing other than the window and document objects.

function getSelectionText() {
    var text = "";
    if (window.getSelection) {
        text = window.getSelection().toString();
    } else if (document.selection && document.selection.type != "Control") {
        text = document.selection.createRange().text;
    }
    return text;
}

If you're interested in an implementation that will also deal with selections in <textarea> and texty <input> elements, you could use the following. Since it's now 2016 I'm omitting the code required for IE <= 8 support but I've posted stuff for that in many places on SO.

function getSelectionText() {
    var text = "";
    var activeEl = document.activeElement;
    var activeElTagName = activeEl ? activeEl.tagName.toLowerCase() : null;
    if (
      (activeElTagName == "textarea") || (activeElTagName == "input" &&
      /^(?:text|search|password|tel|url)$/i.test(activeEl.type)) &&
      (typeof activeEl.selectionStart == "number")
    ) {
        text = activeEl.value.slice(activeEl.selectionStart, activeEl.selectionEnd);
    } else if (window.getSelection) {
        text = window.getSelection().toString();
    }
    return text;
}

document.onmouseup = document.onkeyup = document.onselectionchange = function() {
  document.getElementById("sel").value = getSelectionText();
};

Selection:
<br>
<textarea id="sel" rows="3" cols="50"></textarea>
<p>Please select some text.</p>
<input value="Some text in a text input">
<br>
<input type="search" value="Some text in a search input">
<br>
<input type="tel" value="4872349749823">
<br>
<textarea>Some text in a textarea</textarea>

Get highlighted text this way:

window.getSelection().toString()

and of course a special treatment for ie:

document.selection.createRange().htmlText

This solution works if you're using chrome (can't verify other browsers) and if the text is located in the same DOM Element:

window.getSelection().anchorNode.textContent.substring(
  window.getSelection().extentOffset, 
  window.getSelection().anchorOffset)