What language or technology would I need to be able to create documents online? I want to be able to add text and images and move them into position, resize etc, similar to this.
And then when complete, create a PDF from them.
Sorry if this is a bit vague, I just need to know where to start researching.
You need to decide on your basic technology: Flash, Silverlight, Canvas, client-side SVG, server-side SVG or server-side bitmap. There are also commercial solutions that work with Adobe InDesign documents (and probably a host of other proprietary formats) but I'd expect those not to be cheap.
Flash/Silverlight require plugins, and are considered by some to be a dying technology - though I am sure that is disputed. Canvas is 'very HTML5' and is essentially a bitmap built/rendered on the client, but if you are ultimated rendering to PDF it may not provide the resolution you need. The same limitation affects building an image server-side too - you should probably be dealing with vector elements plus bitmaps, rather than rendering everything to pixels as you go.
That leaves SVG in my list, either on the client (see RaphaelJS) or on the server (see Inkscape). I'm doing some work with server-side SVG rendering at the moment, and it is promising; although subject to more scalability issues than client-side, it doesn't suffer from browser-compatibility issues or the limitations of browser rendering.
The biggest issue in browser SVG rendering is flowed paragraph text and text in/on a path - I am not sure how well these are implemented in modern browsers, or how much agreement there is between them. This is especially the case given that some of these require SVG1.2, and browsers (afaik) are only just settling on SVG1.1, after many years. But, if you just want to do standard blocks of text, bitmaps and vector elements, browser-based SVG should suit you fine.
The example you've given uses a server-side technology (SVG, or perhaps a commercial format) and renders to low-res PNG on the client.
In your case, once you've considered how to 'do the editing', you'll need to consider how to render to PDF, which will be done on the server. You could go low-level and use something like FPDF, use a report renderer like Jasper, or use a graphics system like GhostScript, Inkscape, Scribus, ps2pdf, svg2pdf etc.
Aside: I normally don't answer questions without obvious prior research. But, since you've indicated that you will indeed undertake this, I'm happy to help get you started.