But, but, but: why ANOTHER language??
Rebol - Arturo's ideological grandparent - is a great language (albeit not as well-known as it should be). And Arturo attempts to get the best bits of it and make a modern take on programming.
In the website (and the GitHub repo) you will find more than enough information about it.
Also, have a look at the wiki!
That being said, as I've already mentioned, my goal was not to make a Rebol replica. Arturo is a new language.
Now, regarding the "inspiration" part, to anyone that is familiar with Rebol, I think it would be fair to say that Arturo does look more like the Rebol group, than an Algol-type language, or ML, or Python type of language. I don't know... (I would really be intrigued to hear what it reminds you of... :))
My understanding so far is that Arturo has VM-based interpreter (perhaps stack-based or even indirect-threaded, hence the mention of Forth as an inspiration) which operates on a syntax tree (either concrete or abstract, although Rebol uses the former) produced from textual source during lexing. Is that correct?
Regarding "homoiconicity", the way I would succintly put it is that: the line between what is considered code and what is data is super-fine. Basically, anything can be anything - depending on the context. Thus, an Arturo script can manipulate its own code, the way it can manipulate any other type of data.
Regarding Arturo's implementation: It's written in Nim (though I have written it in the past in almost every language you can think of... lol started with C++, went to D, then to Nim, back to C, and now in Nim again). Basically it's a Stack-based Bytecode Virtual Machine. And yes, Forth's influence is also important - although (intentionally) not that obvious at first sight.
The source text is parsed to an abstract structure/tree of words and symbols. That's the part that happens in translator/parse.
Then if it's an executable block, it is evaluated (as valid Arturo code) into Bytecode (this happens in translator/eval), and then this bytecode is executed by the virtual machine (in vm/exec).