Allah said:

﴿فَمَن شَهِدَ مِنكُمُ الشَّهْرَ فَلْيَصُمْهُ﴾

(So whoever of you sights (the crescent on the first night of) the month (of Ramadan, i.e., is present at his home), he must observe Sawm (fasting) that month.)

This Ayah requires the healthy persons who witness the beginning of the month, while residing in their land, to fast the month. This Ayah abrogated the Ayah that allows a choice of fasting or paying the Fidyah. When Allah ordered fasting, He again mentioned the permission for the ill person and the traveler to break the fast and to fast other days instead as compensation. Allah said:

﴿وَمَن كَانَ مَرِيضًا أَوْ عَلَى سَفَرٍ فَعِدَّةٌ مِّنْ أَيَّامٍ أُخَرَ﴾

(...and whoever is ill or on a journey, the same number ﴿of days which one did not observe Sawm (fasting) must be made up﴾ from other days.)

This Ayah indicates that ill persons who are unable to fast or fear harm by fasting, and the traveler, are all allowed to break the fast. When one does not fast in this case, he is obliged to fast other days instead. Allah said:

﴿يُرِيدُ اللَّهُ بِكُمُ الْيُسْرَ وَلاَ يُرِيدُ بِكُمُ الْعُسْرَ﴾

(Allah intends for you ease, and He does not want to make things difficult for you.)

This Ayah indicates that Allah allowed such persons, out of His mercy and to make matters easy for them, to break the fast when they are ill or traveling, while the fast is still obligatory on the healthy persons who are not traveling.