The PS4 could have earned a majority market share simply by not aggravating consumers and maintaining the same practices, support and policies from the tail end of the PS3 generation, but SCE started with:
Reasonable initial MSRP (Wii U initial MSRP: $299/349), $100 under its key competitor
X86 hardware architecture, shared memory, etc. resulting in a developer friendly platform
One could offer a lengthy list of other reasons why the PS4 became such a success so quickly (SCE admits they were caught off guard as demand/sales exceeded their expectations), but good price and good third party support are at the crux of its success.
Edit: Performance played a fair part on a consumer level. Perception matters, and there was a pretty clear difference in performance on a practical level early on (lower native resolution on many 3rd party titles). The PS4 does have the best hardware this generation, making this arguably the first generation since the SNES that best hardware = best sales (and best hardware had less to do with the SNES' success than great software support).
