HTML + CSS - Overlapping Header Image

I can see three ways to do this generally.

position: absolute

You could give the image or the image's wrapper the attribute of position:absolute and giving its container (in your example the green box) position:relative. Then you would apply top: -100px or whatever and a left attribute of left: 100px or whatever. This gives the effect of the image being out of flow, aligned to the left and offset by 100px, and 100px offset from the top of the green container. The disadvantage of this approach would be that any body content in your green container could appear under the image.

position: relative

This is the same approach as the first one with the exception of how the image flows in the document. Instead of giving the image position:absolute, you would give it position:relative. Relative works differently from absolute. instead of being x and y coordinates of the parent container, it's just shifted by however much you give as a value for top and left. So in this case, you would apply top:-100px and just leave the other directional values as default. this would shift your element by that amount but also leave its original spot in the document flow. As such you end up with a gap below the image that other content will flow around.

negative margin

I honestly would prefer this method in your case. In this method, you can give the image a negative margin (e.g. margin-top:-100px). This will offset the image, collapse the area below the image, and it will still retain some of its flow in the document. This means that the content of the green container will flow around the image but only around the part that is still inside the container. It won't have a ghost area that content flows around like with relative positioning, but it also doesn't entirely take the image out of flow like absolute positioning. One thing to keep in mind, however, is that if you try to use overflow of any kind other than the initial value, it will cause undesirable effects to your image.

Demo

Here's a quick little demo demonstrating all three methods in a simple use case: http://jsfiddle.net/jmarikle/2w4wqfxs/1