TUPE refers to the Transfer of Undertakings (Protection of Employment) regulations, part of UK employment law. It's something best avoided (in the sense of not being a position to need it). It covers such things as transfer of your existing terms and conditions and length of service, etc if you get transferred from one company to another either through outsourcing or a buyout. There's associated redundancy laws and procedures for choosing who gets the chop if it isn't everyone, or a load of procedures to follow if it is everyone.
At first sight it's supposed to protect the employees but as with all laws tryingt o cover the general case, occasionally it definitely is not in the best interest of some.