As marconess says, it's a plug-in for the Chrome Browser (desktop only I'm afraid) that lets you click through to ba.com with the flights you have selected on ITA Matrix. You can search the Chrome webstore for it.

So, to show an example, here's Matrix showing a flight from EDI with an overnight in LHR:



And using the PowerTools plugin, I can click through and purchase those flights on ba.com as shown:


The reason it is cheaper on BA is that Matrix included a GDS fee that BA don't charge on their website, I think from memory that's £8 per sector....