What is a verbal sentence (jumlah fi'liyyah)?
A sentence that opens with a verb is a جُمْلَة فِعْلِيَّة (jumlah fi'liyyah). The verb comes first, and the one who did it comes after.
The verb comes first, then the fā'il who did it — or, when the doer is left out, a nā'ib fā'il standing in its place.
The doer is the فَاعِل (fā'il), and it is always marfū'.
In كَتَبَ مُحَمَّدٌ (kataba muhammadun), “Muhammad wrote”, كَتَبَ is the verb and مُحَمَّد is the fā'il. Arabic puts them in that order; English reverses it.
The doer can be left unnamed. Drop the fā'il from كَتَبَ الدَّرْسَ and you get كُتِبَ الدَّرْسُ (kutiba al-darsu), “the lesson was written” — الدَّرْس now stands in for the missing doer as نَائِب فَاعِل (nā'ib fā'il).
Like most Arabic grammar terms, فِعْلِيَّة (fi'liyyah) was taken from everyday speech and then given one precise technical sense.
In everyday Arabic it simply means “to do with an act”.
جُمْلَةٌ فِعْلِيَّةٌ (jumlatun fi'liyyatun) — “a verb-sentence”
In Arabic grammar it marks the sentence that opens with a verb rather than a noun.