An example may help. Ook! is a small language which makes it fairly easy to write an interpreter for it. For a sample see my attempt at a Perl Ook interpreter. Note that there is no translation to assembly language. A minor translation to an internal representation of the language tokens makes the implementation cleaner, but doesn't generate anything that is new or different than the Ook! source code.

So, how does it work? It works by creating a mini-computer in software (a virtual machine) and runs the code in that environment - no assembly required (or even batteries).