What is offshore outsourcing?

offshore = outside the country
outsourcing = subcontracting parts of a business, paying another company to handle part of your company's work.

offshore outsourcing is what British banks do when they hire companies e.g. in Mumbai, India, to provide call centre services.

The largest complaint of offshore outsourcing for any country is the idea that it's taking away jobs from local citizens. They outsource to foreign countries usually because it's economically more efficient (Cheaper).