Why do Muslims fast in Ramadan?

يَٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُواْ كُتِبَ عَلَيۡكُمُ ٱلصِّيَامُ كَمَا كُتِبَ عَلَى ٱلَّذِينَ مِن قَبۡلِكُمۡ لَعَلَّكُمۡ تَتَّقُونَ ﴿١٨٣﴾ أَيَّامٗا مَّعۡدُودَٰتٖۚ فَمَن كَانَ مِنكُم مَّرِيضًا أَوۡ عَلَىٰ سَفَرٖ فَعِدَّةٞ مِّنۡ أَيَّامٍ أُخَرَۚ وَعَلَى ٱلَّذِينَ يُطِيقُونَهُۥ فِدۡيَةٞ طَعَامُ مِسۡكِينٖۖ فَمَن تَطَوَّعَ خَيۡرٗا فَهُوَ خَيۡرٞ لَّهُۥۚ وَأَن تَصُومُواْ خَيۡرٞ لَّكُمۡ إِن كُنتُمۡ تَعۡلَمُونَ ﴿١٨٤﴾ شَهۡرُ رَمَضَانَ ٱلَّذِيٓ أُنزِلَ فِيهِ ٱلۡقُرۡءَانُ هُدٗى لِّلنَّاسِ وَبَيِّنَٰتٖ مِّنَ ٱلۡهُدَىٰ وَٱلۡفُرۡقَانِۚ فَمَن شَهِدَ مِنكُمُ ٱلشَّهۡرَ فَلۡيَصُمۡهُۖ وَمَن كَانَ مَرِيضًا أَوۡ عَلَىٰ سَفَرٖ فَعِدَّةٞ مِّنۡ أَيَّامٍ أُخَرَۗ يُرِيدُ ٱللَّهُ بِكُمُ ٱلۡيُسۡرَ وَلَا يُرِيدُ بِكُمُ ٱلۡعُسۡرَ وَلِتُكۡمِلُواْ ٱلۡعِدَّةَ وَلِتُكَبِّرُواْ ٱللَّهَ عَلَىٰ مَا هَدَىٰكُمۡ وَلَعَلَّكُمۡ تَشۡكُرُونَ ﴿١٨٥﴾

O you who have believed, decreed upon you is fasting as it was decreed upon those before you that you may become righteous - [Fasting for] a limited number of days. So whoever among you is ill or on a journey [during them] - then an equal number of other days [are to be made up]. And upon those who are able [to fast, but with hardship] - a ransom [as substitute] of feeding a poor person [each day]. And whoever volunteers good [i.e., excess] - it is better for him. But to fast is best for you, if you only knew. The month of Ramaḍān [is that] in which was revealed the Qur’ān, a guidance for the people and clear proofs of guidance and criterion. So whoever sights [the crescent of] the month, let him fast it; and whoever is ill or on a journey - then an equal number of other days. Allāh intends for you ease and does not intend for you hardship and [wants] for you to complete the period and to glorify Allāh for that [to] which He has guided you; and perhaps you will be grateful.