Bootstrap Version 3.x

As always, read Bootstrap's great documentation:

3.x Docs: https://getbootstrap.com/docs/3.3/css/#grid-nesting

Make sure the parent level row is inside of a .container element. Whenever you'd like to nest rows, just open up a new .row inside of your column.

Here's a simple layout to work from:

<div class="container">
    <div class="row">
        <div class="col-xs-6">
            <div class="big-box">image</div>
        </div>
        <div class="col-xs-6">
            <div class="row">
                <div class="col-xs-6"><div class="mini-box">1</div></div>
                <div class="col-xs-6"><div class="mini-box">2</div></div>
                <div class="col-xs-6"><div class="mini-box">3</div></div>
                <div class="col-xs-6"><div class="mini-box">4</div></div>
            </div>
        </div>
    </div>
</div>

Bootstrap Version 4.0

4.0 Docs: http://getbootstrap.com/docs/4.0/layout/grid/#nesting

Here's an updated version for 4.0, but you should really read the entire docs section on the grid so you understand how to leverage this powerful feature

<div class="container">
  <div class="row">
    <div class="col big-box">
      image
    </div>

    <div class="col">
      <div class="row">
        <div class="col mini-box">1</div>
        <div class="col mini-box">2</div>
      </div>
      <div class="row">
        <div class="col mini-box">3</div>
        <div class="col mini-box">4</div>
      </div>
    </div>

  </div>
</div>

Demo in Fiddle jsFiddle 3.x | jsFiddle 4.0

Which will look like this (with a little bit of added styling):