Gut strings are resilient, hold tension better, and players like the feel better. However, humidity affects the strings and cause them to degrade. Gut doesn't last as long as nylon. The compromise is synthetic strings. Basically, gut is made by long thin strands of cow or sheep gut, and it is twisted together in much the same way twine or string is made.
Synthetic gut does the same thing with nylon strings to achieve the same effect.
They cost more than nylon but less than real gut. They play and hold tension better than nylon. Monofilaments are simple, safe, and consistent. Composed of a single, solid core string encased in a thin outer cover, monofilaments are good all-around performers. They hold tension well and offer a pleasing mix of durability and playability.