One machine with many cores will control most of the devices in your house. Wirelessly. Including video and audio feeds.
High end processing will have moved to the cloud for things like games. Latency is low enough and bandwidth high enough to stream everything including live interactive content for the low to mid range.
Because of the single core performance wall, each individual core will not significantly outperform a core of today (probably 50% or so more performance per core over haswell), however, the platform will support many devices by having 16 or 32 cores and the ability to virtualize many terminals into HTPCs, game consoles, internet devices, etc.
Graphics cards and I/O will likely see the largest gains. A 5nm graphics card would be able to cram a lot more parallel processing into a single GPU. This is great because those cards will be able to be virtualized as well and support feeding high quality gaming to multiple TVs in the household.
DDR4 will be an aging standard at this point, and be operating on typical densities of 16-64GB per module.
Flash memory will have come down in price even further, and densities and performance will have increased, driving hard drives out of the market entirely for home use.
4K displays will be standard. OLED / SED / and competing graphics technologies will have risen.