The New Architecture replaces one message queue with direct function calls. It has three parts, plus a code generator that keeps them honest.
JSI (JavaScript Interface) is a C++ API to the JavaScript engine. Native code exposes a C++ host object, and JavaScript holds a real reference to it and calls its methods synchronously, with no JSON in between.
Fabric is the renderer, written in C++ and shared by all platforms. It builds an immutable shadow tree, lays it out with Yoga, diffs it against the previous tree and applies the changes to real views on the UI thread. Immutability lets several trees be in progress at once, which React 7,897 's concurrent rendering needs.
TurboModules are native modules (Kotlin, Swift, Objective-C or C++) reached through JSI. They load on first use instead of at startup, and can return values synchronously.
Codegen turns a TypeScript spec for each module or component into C++ glue and native interfaces at build time, so a type mismatch fails the build instead of crashing a user's phone.

The payoff shows in everyday code: with Fabric, useLayoutEffect reads layout synchronously, so a tooltip appears in the right place in the first frame instead of jumping, and libraries such as VisionCamera pass camera frames to JavaScript as host objects instead of copying them.