"And they worship, instead of God, that for which He has not sent down authority," meaning: proof for their worship. "And of which they have no knowledge," [that is, they have no knowledge] that the idols created anything alongside God, nor did they provide sustenance for anything.
﴿وَيَعْبُدُونَ مِنْ دُونِ اللَّهِ مَا لم ينزل بِهِ سُلْطَانا﴾ يَعْنِي: حُجَّةً لِعِبَادَتِهِمْ ﴿وَمَا لَيْسَ لَهُم بِهِ علم﴾ أَنَّ الْأَوْثَانَ خَلَقَتْ مَعَ اللَّهِ شَيْئا، وَلَا رزقت شَيْئا