Working within a frame
When working on I (intra) frames, which don’t require reference to any other frame when decoding, HEVC offers a wider variety of tools for predicting the content of one block from neighbouring blocks within the frame. H.264, for instance, allowed prediction in any one of eight directions; HEVC provides 33, with a clever concentration of those angles around the horizontal and vertical where real-world pictures are statistically likely to have a lot of similarity.
Motion compensation is a common technique in modern codecs, allowing the re-use of image data which may simply have moved around the frame due to camera motion. With respect to B (bidirectional) and P (predictive) frames, which are assembled with reference to picture data from nearby frames, HEVC provides greater precision than h.264, more accurate processing and a larger range (which is useful for higher-resolution video) when describing where a block of picture may have moved to.
This is where it gets a bit complicated
Moving on to the topic of really complicated mathematics, h.264 allowed either of two final, lossless compression techniques based on entropy coding to be applied to the output of the discrete cosine transform used to compress actual image data. Without turning this article into a pure mathematics lecture, these techniques (CAVLC and CABAC, if you want to look it up) offered a choice of efficiency against CPU horsepower, with CABAC being more effective but rather considerably harder work to decode. This became something of a dividing issue in h.264, with the Baseline and Extended profiles offering only the less effective CAVLC option. Some early video iPod devices supported only these lower profiles, creating an unpalatable choice between performance and bandwidth for distributors. HEVC, on the other hand, requires the more effective CABAC scheme in all cases.
Finally, both h.264 and HEVC provide a couple of types of filtering which correct the output of all the previous operations towards a more ideal result. An in-depth discussion of these filters is beyond the scope of this article, although it’s worth making it clear that these are a lot smarter than simply blurring errors and do make use of information about the picture to clean things up in an intelligent and accurate manner.