The Urbit interpreter is built on a Nock runtime system written in C, u3. This section is a relatively complete description.
You should keep reading if (a) you're planning to work on the Urbit interpreter; (b) you're a language implementation geek; or (c) you don't really understand anything until you've seen the actual structs.
u3: Noun processing in C
u3 is the C library that makes Urbit work. If it wasn't called u3, it might be called libnoun - it's a library for making and storing nouns.
What's a noun? A noun is either a cell or an atom. A cell is an ordered pair of any two nouns. An atom is an unsigned integer of any size.
To the C programmer, this is not a terribly complicated data structure, so why do you need a library for it?
One: nouns have a well-defined computation kernel, Nock, whose spec fits on a page and gzips to 340 bytes. But the only arithmetic operation in Nock is increment. So it's nontrivial to compute both efficiently and correctly.
Two: u3 is designed to be a "solid-state interpreter," ie, a single-level store which is transparently snapshotted. This implies a specialized memory-management model, etc, etc.
(Does u3 depend on the higher levels of Urbit, Arvo and Hoon? Yes and no. u3 expects you to load something shaped like an Arvo kernel, and use it as an event-processing function. But you don't need to use this feature if you don't want, and your kernel doesn't have to be Arvo proper - just Arvo-compatible. Think of u3 as the BIOS and Arvo as the boot kernel. And there are no dependencies at all between Hoon the language and u3.)