Processors understand programs in terms of opcodes - so your intution about executables containing opcodes is correct, and you guessed correctly that any executable has to have opcodes and operands for executing the program on a processor.
However, programs mostly execute with the help of operating systems (you can write programs which do not use an OS to execute, but that would be a lot of unnecessary work) - which provide abstractions on top of the hardware which the programs can use. The OS is responsible for setting up a "context" for any program to run i.e. provide the program the memory it needs, provide general purpose libraries which the program can use for doing common stuff such as write to files, print to console etc.
However, to set up the context for the program (provide it memory, load its data, set up a stack for it), the OS needs to read a program's executable file and needs to know a few things about the program such as the data which the program expects to use, size of that data, the initial values stored in that data region, the list of opcodes that make up the program (also called the text region of a process), their size etc. All of this data and a lot more (debugging information, readonly data such as hardcoded strings in the program, symbol tables etc) is stored within the executable file. Each OS understands a different format of this executable file, since they expect all this info to be stored in the executable in different ways. Check out the links provided by Groo.
A couple of formats that have been used for storing information in an executable file are ELF and COFF on UNIX systems and PE on Windows.
P.S. - Not all programs need executable formats. Look up bootloaders on Google. These are special programs which occupy the first sector of a bootable partition on the hard-disk and are used to load the OS itself.
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