Three things make it possible. The blade is cast as a single crystal with no grain boundaries, because grain boundaries are where a metal creeps and cracks under sustained load at temperature. Cooling air bled from the compressor flows through internal passages and out through hundreds of tiny holes, forming a film that insulates the surface. And a ceramic thermal barrier coating on top drops the metal temperature further.
Each of these is difficult. Single-crystal casting has low yields and takes a long cycle. The cooling holes are drilled by laser or electrical discharge in precise patterns. The coating must survive thermal cycling without spalling. Very few facilities in the world can do all three to the required standard.
They are also three industries rather than one. A foundry that grows single crystals owns vacuum furnaces, ceramic cores and metallurgists; a coating house owns electron-beam evaporators and laser drills and never melts anything; and the ceramic composite route begins with a silicon carbide fibre made by two companies in Japan and is a different material system altogether. When an engine programme is constrained, the constraint sits in exactly one of them.