(as stated by al-Nawawī, Ibn al-Qayyim and Ibn Hajar raḥimahumullāh)
Adhkār is the plural of dhikr and refers to remembrances. The morning and evening adhkār are a collection of du‘ās and remembrances which the Prophet ﷺ instructed us to pray at these two times.
Allah instructed the Messenger of Allah ﷺ in the Qur’ān:
وَسَبِّحْ بِحَمْدِ رَبِّكَ قَبْلَ طُلُوعِ الشَّمْسِ وَقَبْلَ الْغُرُوبِ
“And glorify and praise your Lord before sunrise and before sunset.” (50:39)
The Messenger of Allah ﷺ said: “That I sit with people remembering Allah from Fajr until sunrise is more beloved to me than freeing four slaves from amongst the Children of Ismā‘īl (ʿalayhis-salām). That I sit with people remembering Allah from ‘Asr until the sun sets is more beloved to me than freeing four slaves from amongst the Children of Ismā‘īl (ʿalayhis-salām).” (Abū Dāwūd)
The best time for the morning adhkār is between Fajr and sunrise and the best time for the evening adhkār is between ‘Asr and sunset.
However, if you are unable to recite them during the above times, you can make up for them. For example, if you went back to sleep after Fajr in the summer, then you can make up for them after waking up.
‘The verses of the morning and evening adhkār encourage starting and ending the day with dhikr. This is so that one may commence and end with the worship of Allah, and the dhikr will expiate for the sins perpetrated in between these two periods.’ (al-Nawawī raḥimahullāh)