Video: How phase detection autofocus works
Have you ever wondered how your DSLR's autofocus works? Wonder no more! YouTuber ZY Productions has created a succinct video that details how phase detection autofocus (PDAF) systems work inside DSLR cameras.
As noted in the video, the phase detection autofocus mentioned in this video applies specifically to DSLRs, since it relies on a dedicated autofocus sensor and a translucent section of a DSLR's mirror to achieve focus — components you won't find inside a mirrorless camera.
The exact type of autofocus system depends entirely on what camera you have. Newer DSLRs have robust autofocus systems, with more image coverage and more cross-type focus points — the importance of which is documented in the video — while older cameras might not have as much coverage or as many cross-type focus points (if any at all).
One note we'd add is that Canon's dual cross-type AF points aren't primarily for detecting detail along more axes, but for increasing the precision of these points: with F2.8 and faster lenses, these dual cross-type points allow for more precise focus thanks to their longer baselines.
Regardless of what DSLR you use and how capable its autofocus system is, knowing how your camera's autofocus works and what its shortcomings are should help you to overcome any issues and limitations you come across.
If you'd like a more robust explanation, Photography Life has a great article explaining the process in more detail.