One common practice for decades is to allow a programmer to use source language (whose use may still require extensive training), and have that language translated into object code which the computer can immediately use. The compiling of one into the other varies depending on what CPU is being given the instructions.
Object language in this context means something akin to "the object of what the programmer is trying to achieve". It should not be confused with object-oriented language, which is a type of computer programming language which changes the programmer's environment into convenient objects which can be used in something similar to a drag-and-drop fashion.
Object language in this context is synonymous with target language. The object language of a translation most often is a machine language, but can be some other kind of language, such as assembly language.
Because the object language of compilation has usually been machine language, the term object file has come to mean a file containing machine instructions, and sometimes the translated program itself is simply called an object.
Mathematical logic and linguistics make use of metalanguages, which are languages for describing the nature of other languages. In mathematical logic, the object language is usually a formal language. The language which a metalanguage is used to describe is the object language. It is called that because that language is the object under discussion using the metalanguage.