What counts as a word (al-kalimah)
English needs eight parts of speech to describe itself. Arabic needs three. Reaching that fact takes two steps, and they are the ground everything else in this guide stands on.
Step one — meaningful, or not. Anything a person utters is called لَفْظ (lafz), an utterance. Every lafz is one of two kinds: مَوْضُوع (mawdu'), sound that has been given a meaning, and مُهْمَل (muhmal), sound that has none. Grammar deals only with the first.
Step two — one word, or more than one. The meaningful kind divides again. A كَلِمَة (kalimah) is one meaningful word. A مُرَكَّب (murakkab) is two or more words put together to say what neither could say alone.
The test. كِتَابٌ (kitāb) is a kalimah: the expression carries its meaning whole, and no part of it carries a part of that meaning. كِتَابُ زَيْدٍ (kitābu zayd) is not one word — كِتَابُ carries a share of the meaning and زَيْدٍ carries the rest. That is exactly what مُفْرَد (mufrad), “single”, rules out.
Two senses of كَلِمَة (kalimah). In everyday Arabic it means a speech or a statement — أَلْقَى الْخَطِيبُ كَلِمَةً, “the speaker delivered an address”. In grammar it means exactly one word. Both are correct; this guide always means the second.
From the free course The Language of Quran — Easier than English (Book 1) (LoQ1), taught by Ustadh Muhammad Arjan Ali.
Is كِتَابُ زَيْدٍ (kitābu zayd) one word or two?
Two. Each half carries a share of the meaning, so it fails the test of مُفْرَد (mufrad). It is a مُرَكَّب (murakkab) — a possessive phrase.