Your first line addresses two points where Native Client provides utility. NaCl is good for C/C++/assembly coders to bring an application written in their language of choice to the web, and NaCl helps applications run faster/with better performance/more efficiently (aka with less use of battery). Native Client also provides threaded applications, allowing programming models (and the performance that goes along with threads) to run natively on the web (aka not with web workers).
The Sockets API is available to all chrome packaged apps, the distinction is that the API makes the sockets directly to a NaCl application, which is faster and has the benefit of porting existing native applications to the browser without modifications. There are also a variety of other APIs, like Game controllers, hardware decode (coming soon), and Fullscreen/Mouselock. Find the full list of Pepper APIs that enable NaCl capabilities here: https://developer.chrome.com/native-client/pepper_stable/c/index#pepper-stable-c-index.
For Portable Native Client, the most notable capabilities are the ability to use threading, and portable intrinsics (SIMD). Perhaps writing core logic that can run cross-platform (aka a C/C++ "model" that can interact with different views on different platforms) isn't a strict capability, but it is a benefit of using NaCl, especially for developers also using Objective C/Android NDK to build native mobile versions of their application.