What is a complete construct (murakkab tām)?
Join two or more words so that together they give a meaning, and you have a مُرَكَّب (murakkab). When the meaning is complete, the murakkab is تَامّ (tām).
The test is whether the meaning stands on its own. The speaker can stop there, and the listener is not left waiting.
كِتَابُ مُحَمَّدٍ (kitābu muhammadin), “Muhammad’s book”, leaves the listener waiting. أَقْبَلَ ضَيْفٌ (aqbala dayfun), “a guest arrived”, does not. Two words, and nothing is missing.
A complete construct is a sentence. The books of grammar call the same thing الْجُمْلَة (al-jumlah) and الْكَلَام (kalām).
A jumlah is one of two: ismiyyah, which opens with a noun; or fi'liyyah, which opens with a verb.
أَقْبَلَ ضَيْفٌ (aqbala dayfun) opens with a verb. This is called جُمْلَة فِعْلِيَّة (jumlah fi'liyyah). الضَّيْفُ كَرِيمٌ (al-dayfu karīmun), “the guest is generous”, opens with a noun. This is called جُمْلَة اِسْمِيَّة (jumlah ismiyyah).
Like most Arabic grammar terms, تَامّ (tām) was taken from everyday speech and then given one precise technical sense.
In everyday Arabic it means complete — a thing with nothing left out.
شَهْرٌ تَامٌّ (shahrun tāmmun) — “a full month”
In Arabic grammar it describes a murakkab whose meaning is complete, so that it stands as a sentence.