Offshoring is business jargon. It sounds like a nice seaside vacation, doesn’t it? What it means is: setting up shop (generally a factory or a call center) in a country where people will work for a lot less money than they would in your company’s country of origin.
There are all kinds of complicated arguments about whether this is a good thing to do or not. I’m not going to get into any of them here, but I will say that wherever you find a word like this — an image so dramatically different from the thing it is supposed to describe — chances are pretty good that you’ll also find an unrepentant spin doctor or a guilty conscience.