We know that Holy Prophet's()father name was Abdullah & he had passed away before Prophet's birth.With this background please tell that what was the concept in arabs about "ALLAH"before prophet.Were they familiar to this word before prophet's birth?How did they differentiate Allah from idols,if at all they did?
You should note that Arabian societies before Islam were not atheistic societies that denied the existence of Allaah, or societies that were unaware that there is a Lord, Creator and Provider. They knew that, and they still retained some traces of the religion of Ibraaheem, and they had contact with Jews and Christians. But their problem was that they did not worship Allaah Alone in exclusion to others; they had other gods whom they associated in worship with Him, and which they worshipped not on the basis that they were the Lord, the Creator the Provider, but because they claimed that these were intermediaries who would intercede between them and Allaah and bring them closer to Allaah. Hence Allaah said concerning them (interpretation of the meaning):
“And if you (O Muhammad) ask them: ‘Who has created the heavens and the earth,’ they will certainly say: ‘Allaah’” [Luqmaan 31:25]
This indicates that they acknowledged that Allaah is the Creator. Another aayah says (interpretation of the meaning):
“And verily, if you ask them: ‘Who created the heavens and the earth?’ Surely, they will say: ‘Allaah (has created them)’”
Many aayaat indicated that they believed in the Unity of Lordship (Tawheed al-Ruboobiyyah); their shirk was with regard to divinity (uloohiyyah), as Allaah says concerning them (interpretation of the meaning):
“And those who take Awliyaa’ (protectors, helpers, lords, gods) besides Him (say): ‘We worship them only that they may bring us near to Allaah’” [al-Zumar 39:3]
i.e., they said, we only worship them so that they may bring us closer to Allaah.