Rotate with Shapes is an option that you can check when configuring the background of a shape or the slide background in a PowerPoint presentation. This option is available for example under the Format Picture dialog when you choose Fill and options like Fill by picture or texture fill. It is also available when you choose a gradient fill.
But, what this option Rotate With Shapes means? Basically what you can configure by checking this option is to make possible to rotate the background along with the shape rotation. This is why sometimes when you configure the general powerpoint background you may see that the checkbox is disabled. This is because the checkbox is only enabled when you configure the background and fill options of a shape and not the entire powerpoint background.
To enable Rotate with shape checkbox like in the picture you will need to select a shape and not the PPT background. You can also learn more about rotating shapes in powerpoint 2010.