Direct object (maf'ul bih)
After the doer, many verbs need a receiver of the action. That receiver is the maf'ul bih, marked in nasb (fatha or its substitute). It may be a noun, or a pronoun attached to the verb, and it can be fronted for emphasis.
Both مفعول مطلق and حال are also in nasb: the first repeats the verb's own meaning, the second answers “how?”. The maf'ul bih answers “whom/what?”.
Must the object come after the verb?
No — it can be fronted for emphasis (إِيَّاكَ نَعْبُدُ) or attached as a pronoun. The nasb ending, not the position, identifies it.
Why can't هُوَ or أَنْتَ be the object of a verb?
The detached pronouns are fixed in raf' — subjects only. Arabic supplies the attached set for nasb positions: “he helped him” must be نَصَرَهُ, never نَصَرَ هُوَ.
Can a verb take two objects — or none?
A few take two, both in nasb: جَعَلَ اللهُ مُحَمَّدًا رَسُولًا. And intransitive verbs (ذَهَبَ، جَلَسَ) take none at all — their action stays with the doer.