What is the meaning of "دبر كل صلاة" (at the end of every prayer), and does it mean before the Tasleem or after it, and is it sunnah to raise the hands in supplication after the prayer?

The term "dubur al-salat" (end/rear of the prayer) refers to both the very end of the prayer, before the taslim (salutation of peace), and the period immediately after it. The authentic hadiths (prophetic traditions) have come with both meanings:

1. The end of the prayer before the taslim: This is intended if it is a du'a (supplication), as in the hadith of Mu'adh: "O Allah, help me to remember You, to thank You, and to worship You in the best manner," and the hadith of Sa'd ibn Abi Waqqas: "O Allah, I seek refuge in You from stinginess...", and the hadith of Abu Umamah: "Which supplication is most heard? He said: 'The last third of the night, and after the prescribed prayers.'"

2. Immediately after the taslim: This is intended if it is a dhikr (remembrance of Allah), such as tasbih (glorification), tahmid (praise), takbir (magnification), reciting Ayat al-Kursi, and the Mu'awwidhat (protective surahs), as in the hadith of Al-Mughirah ibn Shu'bah: "There is no god but Allah alone, without partner...", and the hadith of Abu Hurayrah concerning tasbih, tahmid, and takbir after the prayer, and the Prophet's (peace be upon him) saying: "I seek Allah's forgiveness" three times.

Scholars have mentioned that what is a dhikr at the end of the prayer is performed after it, and what is a du'a is performed at its very end before the taslim, except for what has a specific text stating that it is to be said after the taslim.

It is not legislated to raise the hands in du'a after the prayer; this is because it has not been reported from the Prophet (peace be upon him).