A compiled program usually contains a header followed by valid CPU instructions (what you can call "binary") + various other data.
When you try to tell the OS to load your program, the header will be read by the OS, and it will be used to verify that the executable is a really executable file for that OS and this architecture. That is, so that you do not accidentally run a Linux program on Windows or similar.
The header also contains various other bits of information about where the actual processor instructions are in the exeutable file, where the data segments are located (text, lines, graphics), etc.
Once the OS is happy that the executable is what it should be, then the OS will load the different segments from the executable into memory and instruct the CPU to run the “binary” code segment. This code is "clean" in a sense that it is direct processor assembly code.
However, the operating system may interrupt the processor (for example, switch to another program or simply kill the program from memory, etc.). Thus, there are a lot of things in this running program, and the kind of OS “controls” it and ensures that it behaves like a good boy, but the code itself, when it is running, executes clean processor instructions as quickly as possible .. without using the OS to interpret the code between them.
Also note that a running program can call the OS differently while it is running. For example, to request the OS to open a window on the display, open a network connection, allocate memory, etc. All that actually happens is that the processor simply proceeds to execute the code elsewhere (i.e., it jumps from running the code in the executable file, runs part of the code in the OS, and then jumps back).
What is this in a nutshell. However, there are many other ways to run programs. There are virtual machines, interpreted languages (e.g. Java or Ruby), etc. And they all run programs differently from traditional “pure binary” languages like C / C ++, but hopefully this helps you understand how this works a little better.