function highlight_text_nodes($nodes, word) {
  if (!$nodes.length) {
    return;
  }

  var text = '';

  // Concatenate the consecutive nodes to get the actual text
  for (var i = 0; i < $nodes.length; i++) {
    text += $nodes[i].textContent;
  }

  var $fragment = document.createDocumentFragment();

  while (true) {
    // Tweak this if you want to change the highlighting behavior
    var index = text.toLowerCase().indexOf(word.toLowerCase());

    if (index === -1) {
      break;
    }

    // Split the text into [before, match, after]
    var before = text.slice(0, index);
    var match = text.slice(index, index + word.length);
    text = text.slice(index + word.length);

    // Create the <mark>
    var $mark = document.createElement('mark');
    $mark.className = 'found';
    $mark.appendChild(document.createTextNode(match));

    // Append it to the fragment
    $fragment.appendChild(document.createTextNode(before));
    $fragment.appendChild($mark);
  }

  // If we have leftover text, just append it to the end
  if (text.length) {
    $fragment.appendChild(document.createTextNode(text));
  }

  // Replace the nodes with the fragment
  $nodes[0].parentNode.insertBefore($fragment, $nodes[0]);

  for (var i = 0; i < $nodes.length; i++) {
    var $node = $nodes[$nodes.length - i - 1];
    $node.parentNode.removeChild($node);
  }
}


/*
 * Highlights all instances of `word` in `$node` and its children
 */
function highlight($node, word) {
  var $children = $node.childNodes;
  var $current_run = [];

  for (var i = 0; i < $children.length; i++) {
    var $child = $children[i];

    if ($child.nodeType === Node.TEXT_NODE) {
      // Keep track of consecutive text nodes
      $current_run.push($child);
    } else {
      // If we hit a regular element, highlight what we have and start over
      highlight_text_nodes($current_run, word);
      $current_run = [];

      // Ignore text inside of our <mark>s
      if ($child.nodeType === Node.ELEMENT_NODE && $child.className !== 'found') {
        highlight($child, word);
      }
    }
  }

  // Just in case we have only text nodes as children
  if ($current_run.length) {
    highlight_text_nodes($current_run, word);
  }
}

/*
 * Removes all highlighted <mark>s from the given node
 */
function unhighlight($node) {
  var $marks = [].slice.call($node.querySelectorAll('mark.found'));

  for (var i = 0; i < $marks.length; i++) {
    var $mark = $marks[i];

    // Replace each <mark> with just a text node of its contents
    $mark.parentNode.replaceChild(document.createTextNode($mark.childNodes[0].textContent), $mark);
  }
}



var $p = document.querySelector('p');

document.querySelector('input').onkeyup = function() {
  unhighlight($p);

  if (this.value.length) {
    highlight($p, this.value);
  }
};

<input type="text" />

<p>
<b>JavaScript</b> is a high-level, dynamic, multi-paradigm, object-oriented, prototype-based, weakly-typed language traditionally used for client-side scripting in web browsers. JavaScript can also be run outside of the browser with the use of a framework like Node.js, Nashorn, Wakanda, or Google Apps Script. Despite the name, it is unrelated to the Java programming language and shares only superficial similarities.

Unless a tag for a framework or library is also included, a pure JavaScript answer is expected for questions with the javascript tag.
</p>