Tawhid (توحيد), meaning "declaring God one", is the Islamic concept of monotheism. Its opposite, comprehending the sins of polytheism and idolatry, is shirk, where more information can be found.
Tawhid has three aspects: Tawhid ar-Rububiyya, Tawhid al-Asma wa as-Sifat and Tawhid al-ibada.
Tawhid ar-Rububiyya is the conviction that God, and only God, creates and sustains the universe, that without his will the universe could not continue to exist. Failure to hold this conviction results in either polytheism or atheism.
Tawhid al-Asma wa as-Sifat is the conviction that God has certain names and characteristics which He mentioned in the Quran or in the sayings of the Prophet Muhammad (Sunnah). It is the belief that nothing resembles God, nor does He resemble any of His creation.
Tawhid al-ibada means "declaring God one through our service", to worship God and only God both in those actions that are visible to others and in those actions and thoughts that are hidden from other men. This requires one to worship God alone, with pure and sincere intent and dedication. Worship includes any action done in servitude to God which he commanded, such as prayer, supplication, sacrifice, vowing, love and fear.
Thus true monotheism in Islam requires one to have the correct knowledge (tawhid ar-rububiyya), the correct understanding (tawhid al-asma wa as-sifat), and the correct motivation (tawhid al-ibada).
However, an aspect of Tawheed that perhaps needs to be stressed in particular is Tawheed ul-`Ibaadah, as it is often either not understood properly or is neglected to a varying degree.
Tawheed ul `Ibaadah is to single-out Allah alone for all worship and not to worship anything along with Him, whether it be an angel, a Messenger, a Prophet, a pious person, a tree, a stone, the sun, the moon, or other than these, such as money or one's desires.
It is this aspect of Tawheed that the Prophets were sent to elaborate first and foremost, "And verily, We have sent amongst every nation a messenger (with the command): 'Worship Allah and avoid all false deities" [16:36].