Superconductors are materials whose electrical resistance drops to zero when they are cooled far enough, there are low temperature superconductors which normally work at below -263 celcius or 10 degrees above absolute zero, these are often conventional metals and are easy to bend but need immensely good insulation to keep them that cold, and there are high temperature superconductors which can work at 77 degrees above absolute zero, which is far easier to achieve. They would be ideal for carrying current but unfortunately but they are all brittle ceramics, similar physically to china, which makes making cables very difficult. The only way to make them at all flexible is to use very thin pieces of superconductor, making them reasonably flexible. Despite this most superconducting cables are still so brittle they have to be wound around large formers making them very very inflexible.
Danko van der Laan has improved this significantly by using a slightly different superconductor called Gadalinium barium Copper Oxide or GBCO, whose superconducting properties are no better than other superconductors, but it degrades much more slowly when it is bent slightly. This has allowed him to wind his superconducting tapes around a copper former that is only about 6mm in diameter this along with the advantages of the GBCO means that the final cable is much more flexible. They have managed to sucessfully bend it around a diameter of 25cm whilst still being able to carry 1200A of current which is about half the current carried by a large electricity pylon. Of course to actually do this the cable would have to be electrically insulated and cooled, but it could still be far smaller, lighter and easier to install than current cables, making them practical for installing in ships and possibly even aircraft