Auto-key is like having Houdini automatically press K (keyframe) for you when you make a change. So, it automatically sets keys when you change parameters with existing channels.
This lets you scrub the playbar, move objects, pose characters, etc. without having to remember to set or commit keys. However, you can also accidentally create unintended keys/animation.
To turn auto-key on or off, click the Auto-key icon on the playbar, or choose Edit ▸ Preferences ▸ Animation and use the Auto-key option.
Auto-key is related to two other preferences under Edit ▸ Preferences ▸ Animation:
Auto-commit is similar to Auto-key, but controls whether Houdini automatically commits changes when a key already exists at the current frame.
Important: when this option is on, when you (for example) key the position of an object, you must change the time before you reposition the object for the next key. If you reposition the object before you change the time, because of the auto-commit setting, you will have changed the keyed values.
Global set key controls whether Houdini automatically keys/commits all pending changes, or only the scoped parameters.