Laa ilaaha illallaah has 2 pillars

Laa ilaaha illa Allaah à none has the right to be worshipped except Allaah, and anything that is worshiped besides Him is done so in falsehood. 

This statement has two pillars that make it complete. Both pillars have to be attested to for a person to be considered a Muslim. 

1^st Pillar:   Negation: Laa ilaaha – none has the right to be worshipped
The first pillar is to negate and deny any worship as well as all forms of divinity attributed to other than Allaah 

2^nd Pillar:   Affirmation: illa Allaah – except Allaah
The second pillar is to affirm that all worship and attributes of divinity is for Allaah alone 

Therefore one must negate, deny, and disbelieve that anything should be worshipped besides Allaah, and affirm and believe that it is only Allaah that possess attributes of divinity and is deserving of worship by Himself subhaanahu wa ta’alaa (far removed is He from any imperfection, the Most High).  This meaning along with its pillars came in the Quran. In Souratul Baraqarah (chapter 2) Verse 256 Allaah the Most High says: 

فَمَنْ يَكْفُرْ بِالطَّاغُوتِ وَيُؤْمِن بِاللّهِ

“Whoever disbelieves in Tâghût and believes in Allâh, then he has grasped the most trustworthy handhold that will never break” [2:256] 

NOTE:          The word Tâghût covers a wide range of meanings: It means anything worshipped other than the Real God (Allâh), but the one who does not accept to be worshipped will not be considered as a Tâghût, i.e. all the false deities. It may be Satan, devils, idols, stones, sun, stars, angels, human beings, who were falsely worshipped and taken as Tâghûts. Likewise saints, graves, rulers, leaders, etc., are falsely worshipped and wrongly followed. Sometimes “Tâghût” means a false judge who gives a false judgement (see V.4:60). [See Tafsir Ibn Kathir and (V.4:51)]. If the one worshiped is not pleased with it, he is not considered a taghoot. Eg. Prophet Essa (Jesus) is not a taghoot eventhough he is worshiped.

In another ayah in Souratu az-Zukhruf, verses 26-27, Allaah tells us of Prophet Ibrahim’s (alayhis-salam) saying to his father who was an idol worshipper: 

وَإِذْ قَالَ إِبْرَاهِيمُ لِأَبِيهِ وَقَوْمِهِ إِنَّنِي بَرَاء مِّمَّا تَعْبُدُونَ / إِلَّا الَّذِي فَطَرَنِي فَإِنَّهُ سَيَهْدِينِ

“And (remember) when Ibrâhîm (Abraham) said to his father and his people: ‘Verily, I am innocent of what you worship, Except Him (i.e. I worship none but Allâh Alone) Who did create me; and verily He will guide me.” [43:26-27] 

In both verses there is firstly a negation/disbelief in anything being worshipped besides Allaah, and then there is an affirmation of making worship only for Allaah “except Him who created me”. 

This affirmation is also present in souratul-Faatiha when we say:

إِيَّاكَ نَعْبُدُ وإِيَّاكَ نَسْتَعِينُ

-You (Alone) we worship, and You (Alone) we ask for help (for each and everything).