Prepending textbox to Wikipedia thumbnail picture
Nice idea.
Here's a solution that breaks down each of the steps into tiny, single purpose functions, whose names reveal exactly what they do.  This removes all the nesting and makes the solution easier to follow.
New logical steps:

Identifying a valid link (this was always broken out in the oringal solution)
&quot;Upgrading&quot; a link into a preview link (this is no longer coupled to 1., and can be re-used for other links)
Fetching the link's html
Extracting just the body text from the html
Filling the preview window with text

Some ideas that might be nice:

It might be nice to have the preview window vanish if you click the same link again.
Remove old contents from preview window, rather than prepending

Other notes:

I put the each statement that kicks everything off at the bottom, so that you can still copy paste into the console, even though it's more logical to have it at the top, since it's the &quot;main&quot; method, so to speak.
I removed the alerts, since I didn't think they were necessary.

Refactored code:
function turnIntoPreviewLink(link) {
  $(link).click(function(e) { e.preventDefault(), previewContents(link.href); })
}

function previewContents(wikiUrl) {
  grabHtml(wikiUrl).done(function(html) {
    addContentToPreview(bodyText(html));
  })
}

function grabHtml(wikiUrl) {
  return $.ajax({ type: 'get', url: wikiUrl });
}

function bodyText(html) {
  return $(html).find('#bodyContent #mw-content-text p').text();
}

function addContentToPreview(text) {
    $(&quot;.infobox .vcard .plainlist&quot;).addClass($(&quot;.infobox tbody&quot;).prepend(text));
}
  
function isValidWikiPage(url) {
  return url.indexOf('wikipedia.org') &gt;= 0;
}

$(&quot;a&quot;).each(function(i, link) {
  if (isValidWikiPage(link.href)) turnIntoPreviewLink(link);
});