It is difficult to know what is actually new information in this Intel blog post, but it is interesting none-the-less. Its topic is the AVX-512 extension to x86, designed for Xeon and Xeon Phi processors and co-processors. Basically, last year, Intel announced "Foundation", the minimum support level for AVX-512, as well as Conflict Detection, Exponential and Reciprocal, and Prefetch, which are optional. This, earlier blog post was very much focused on Xeon Phi, but it acknowledged that the instructions will make their way to standard, CPU-like Xeons at around the same time.

This year's blog post brings in a bit more information, especially for common Xeons. While all AVX-512-supporting processors (and co-processors) will support "AVX-512 Foundation", the instruction set extensions are a bit more scattered.

 
Xeon
Processors
Xeon Phi
Processors
Xeon Phi
Coprocessors (AIBs)
Foundation Instructions Yes Yes Yes
Conflict Detection Instructions Yes Yes Yes
Exponential and Reciprocal Instructions No Yes Yes
Prefetch Instructions No Yes Yes
Byte and Word Instructions Yes No No
Doubleword and Quadword Instructions Yes No No
Vector Length Extensions Yes No No

Source: Intel AVX-512 Blog Post (and my understanding thereof).

So why do we care? Simply put: speed. Vectorization, the purpose of AVX-512, has similar benefits to multiple cores. It is not as flexible as having multiple, unique, independent cores, but it is easier to implement (and works just fine with having multiple cores, too). For an example: imagine that you have to multiply two colors together. The direct way to do it is multiply red with red, green with green, blue with blue, and alpha with alpha. AMD's 3DNow! and, later, Intel's SSE included instructions to multiply two, four-component vectors together. This reduces four similar instructions into a single operating between wider registers.

Smart compilers (and programmers, although that is becoming less common as compilers are pretty good, especially when they are not fighting developers) are able to pack seemingly unrelated data together, too, if they undergo similar instructions. AVX-512 allows for sixteen 32-bit pieces of data to be worked on at the same time. If your pixel only has four, single-precision RGBA data values, but you are looping through 2 million pixels, do four pixels at a time (16 components).

For the record, I basically just described "SIMD" (single instruction, multiple data) as a whole.

This theory is part of how GPUs became so powerful at certain tasks. They are capable of pushing a lot of data because they can exploit similarities. If your task is full of similar problems, they can just churn through tonnes of data. CPUs have been doing these tricks, too, just without compromising what they do well.