It does this by having slightly different code in the .Net Core Framework and Runtime for different platforms.
.NET compiles down to IL (Intermediate language) which is a pseudocode. It is then JIT (just in time) compiled to platform specific code. As long as you have a JIT compiler that can compile to a platform, you can push to that platform. For Linux it was originally called Mono. Microsoft eventually bought the project out, which was actually a good thing, as we ended up with platform parity.