The translation of salat into ‘prayer’ is only partially correct, as the Arabic word for this is du¢ā’, and can refer to any form of prayer performed anywhere and under any circumstance. Salat however can only be performed with standard movements, and in conjunction with one of the day’s 5 prayer moments.
Salat appears not to have occurred in Mecca before Muhammad, and according to Western scholars, he must have gotten the principle from Christians and Jews.
Salat is mentioned several times in the Koran, both on its intent, when to do it, and how to:
Koran sura 2: The Cow
42 Ask for help in patience and prayer. That is hard, except for the humble.239 Attend regularly to your prayers, including the middle one. Stand up for God with all your devotion.
Koran sura 4: Women
46 You who believe, do not perform your prayers when you are drunk, you will not know the meaning of what you say. Nor when you are polluted, unless you are travelling, until you have washed yourselves. If you are ill or travelling and cannot wash yourselves, or you have relieved yourselves, or had sex with women and can find no water, then take some fine sand and rub your faces and your hands with it. God is gracious and forgives.
Koran sura 17: Night Journey
80 Recite your prayers at sunset, at nightfall and read from the Koran at dawn. The dawn prayer has its witnesses.
110 Say: Call on God or call on the Merciful. No matter what you call him, to him belongs the most gracious names. Do not pray too loud, nor should you whisper, seek a middle course.