Ḥāl: a circumstantial accusative expression, or a clause occupying the accusative slot.
Ṣāḥib al-ḥāl: the person or thing whose state is described.
ʿĀmil al-ḥāl: the verb or verbal meaning that governs the circumstance.
In «جَاءَ زَيْدٌ رَاكِبًا», Zayd is the referent, rākiban the ḥāl, and jāʾa the governor.