The legislated meaning of Monotheism:
‘Singling out Allaah The Glorified, in Lordship, Worship and Names & Attributes.’
Meaning that you only worship Allaah alone, you do not worship anything in association with Him, rather you only worship Him, in love of Him, Glorifying Him, yearning for His reward and fearing His punishment.
It is this for the establishment of this monotheism that Allaah sent the messengers again and again to re establish it. Quran is replete with verses concerning monotheism i.e. worshipping ALLAH alone, invoking ALLAH alone, submitting to ALLAH alone, and believing only in ALLAH as THE ONE WHO HAS ALL THE POWERS.
And verily, We have sent among every Ummah (community, nation) a Messenger (proclaiming): "Worship Allâh (Alone), and avoid Tâghût (all false deities, i.e. do not worship anything besides Allâh)." [surah Nahl, chp:16, v:36] And We did not send any Messenger before you (O Muhammad [sal-Allâhu 'alayhi wa sallam]) but We revealed to him that “none has the right to be worshipped but I (Allâh)”, so worship Me (Alone and none else)." [021:025] Messengers are bearers of good news as well as of cautioners (of bad consequences) in order that mankind should have no plea against Allâh after the (coming of) Messengers. And Allâh is Ever All-Powerful, All-Wise. [Surah Nisa, chp:04, v:165]
Thel definition for monotheism, it is:
‘Singling out Allaah, the Elevated, with what is specific to Him in three things [Lordship, worship and Names and Attributes]:
The First: Monotheism of Lordship (Tawheed ar Rububiyyah):
It is to single out Allaah the Elevated with creation, ownership and the disposing of all affairs.
Allaah the Glorified said: Allaah is the Creator of all things… [Az Zumar: 62] He also said: Is there any creator other than Allaah who provides for you from the sky (rain) and the earth? La ilaaha illa Huwa (none has the right to be worshipped but He). [Faatir: 3] He said: Blessed is He in Whose Hand is the dominion; and He is Able to do all things.[Al Mulk: 1] He said: Surely, His is the creation and commandment. Blessed is Allaah, the Lord of the 'Alameen (mankind, jinn and all that exists)! [Al ‘Araaf: 54]