AVX Intrinsics refers to Intel's Advanced Vector Extensions, which allows you to code for vectorization. Vectorization is the idea that each processor core can operate on multiple values (a vector) simultaneously per instruction cycle. Some compilers do some auto-vectorization, but it's better if the programmer specifies vectorization to help the compiler out.
From reading the Wikipedia page on SIMD, I learned that Swift 2.0 has SIMD Vectors support. Here is an interesting blog post with some examples. This video also talks more about SIMD in Swift. The additions help abstract intrinsics, which is kind of nice.
How similar is this vector syntax this to MATLAB data types?