When we hear the word dawah, we tend to automatically associate it with calling non-Muslims to Islam. But this is only one of the meanings that it can bear.
Linguistically, دعوة da’wah comes from the same root as دعاء du’aa - د ع و. This root, in its most basic form, alludes to the meaning of making something incline towards you using sound or speech.
So when we make du’a, we ask Allah to incline towards what we are requesting of Him and to grant us that request. And when we do da’wah - in the way we know it - of calling people to Islam - we try to make them incline towards what we are calling to, using our words. As He says in Surah Fussilat, verse 33,
وَمَنْ أَحْسَنُ قَوْلًۭا مِّمَّن دَعَآ إِلَى ٱللَّهِ وَعَمِلَ صَـٰلِحًۭا وَقَالَ إِنَّنِى مِنَ ٱلْمُسْلِمِينَ
Who speaks better than someone who calls people to God, does what is right, and says, ‘I am one of those devoted to God’?
In this verse, Allah praises those who call to Islam with good speech and action. It is interesting to view this word in light of the linguistic phenomenon of ‘al-ishtiqaaq al-kabeer’ (aka al-qalb al-makaani) - wherein we find two words having the same root letters but in a different sequence, and also sharing meaning. We can then contemplate that the letters of the root د ع و transpose to form the root و ع د, which connotes giving someone hope of something (good or bad). Allah uses the verb وَعَدَ (‘he promised’) in Surah Ma’idah verse 9,
وَعَدَ ٱللَّهُ ٱلَّذِينَ ءَامَنُوا۟ وَعَمِلُوا۟ ٱلصَّـٰلِحَـٰتِ ۙ لَهُم مَّغْفِرَةٌۭ وَأَجْرٌ عَظِيمٌۭ
Allah has promised those who believe and do good His forgiveness and a great reward.
Thus we can see how the two roots are linked - making a promise (of good or bad) is one way of making a person incline towards doing something.
Allah chose this beautiful language of Arabic as the medium of conveying His message to us, and we can see how exploring the relationship between roots and meanings of words can deepen our understanding of Islamic concepts and His message.
While there have been extensive works written on the language, there still remain more dimensions of it to explore.
And Allah knows best.