What is a demonstrative phrase (murakkab ishārī)?

One word points, the other is pointed at. The pointing word is the اِسْم إِشَارَة (ism ishāra); the thing pointed at is the مُشَار إِلَيْه (mushār ilayh).

The ism ishāra does the pointing; the mushār ilayh is the noun pointed at, and it carries ال.

In هَٰذَا الْكِتَابُ (hādhā al-kitābu), “this book”, هَٰذَا points and الْكِتَاب is what it points at. The noun pointed at carries ال.

Arabic chooses the pointing word by distance and by the noun itself. هَٰذَا is for what is near, ذَٰلِكَ for what is far, and both change for gender and number.

Like most Arabic grammar terms, إِشَارَة (ishāra) was taken from everyday speech and then given one precise technical sense.

In everyday Arabic it means a sign or a gesture.

أَشَارَ بِيَدِهِ (ashāra bi-yadihi) — “he gestured with his hand”

In Arabic grammar it means a word that points at the noun beside it.