The wires and strings are both displayed using Mathematica's built-in Tube and BsplineCurve commands.
The examples provided are wire-and-string puzzles invented by the author in 1993. The task in these puzzles is to remove the closed string from the closed wire loop without cutting the string.
In this Demonstration an elastic string is used for convenience, but this has no influence on the validity of the solutions.
The Demonstration "3D Curve Constructor" by the same author shows several wire-and-string puzzles (in their entangled state) as examples.
The Demonstration "Wire-and-String Puzzles" by the same author lets you play with and solve these puzzles, but the presentation of the puzzles is two-dimensional and very simplified.
The real wire-and-string puzzles are manually created from copper or steel wire. Silver plated and produced in small sizes, some puzzle types are flat enough to be worn as pendants around your neck as puzzle jewelry.
In this case a narrow black ribbon is used instead of a string.