This is a punning reference to the longer-established term tiger economy, which has been used for about fifteen years to describe the more successful small Asian economies. The original tiger economies were the Four Tigers of Hong Kong, Singapore, Taiwan and South Korea, which have been joined more recently by others that include the Philippines, Thailand and Malaysia (though these, with Hong Kong, have suffered substantial economic reverses this year, which have affected many Western financial markets).
The Celtic Tiger is the Republic of Ireland, which has benefited very greatly from its membership of the European Union, both through financial aid and through inward investment by companies opening factories in the country to gain access to European markets and take advantage of the country’s low rate of corporation tax. As a result, Ireland claims to have been the fastest-growing economy in Europe over the past decade, admittedly from a low base (though some critics claim the figures have been inflated through a sneaky tendency of some multinationals to pretend output comes from Ireland in order to pay less tax, a technique known as transfer pricing). The term is mostly confined to British and Irish business and financial circles, and must be classed as jargon.