Saḥūr is the pre-dawn meal that is consumed in the blessed month of Ramaḍān prior to fasting, and it is called that because the meal is consumed at the time of saḥār which is shortly before dawn. Allāh said:

كَانُوا قَلِيلًا مِّنَ اللَّيْلِ مَا يَهْجَعُونَ ‎﴿١٧﴾‏ وَبِالْأَسْحَارِ هُمْ يَسْتَغْفِرُونَ ‎﴿١٨﴾

“They would only sleep a small part of the night, and at the time of saḥar [i.e. the time just before dawn], they would seek forgiveness.”
[Al-Dhāriyāt, 51:17-18]

Ibn Ḥajr (رحمه الله) said: “Saḥar is the last part of the night [i.e. the time just before dawn], and saḥūr is the meal consumed at that time.” (Fatḥ al-Bārī, vol. 1, pg. 130)

Zayd ibn Thābit (رضي الله عنه) narrated: “We had saḥūr with the Prophet (ﷺ). He then stood to perform the prayer.” (Reported by al-Bukhārī)

Standing moments after the consumption of the meal to perform the Fajr prayer proves that saḥūr is consumed shortly before dawn. Therefore, saḥūr is the meal that is consumed in the blessed month shortly before dawn.

Saḥūr is also called falāḥ, like al-falāḥ in the muʿadhdhin’s statement: “Ḥayyá ‘alá al-falāḥ,” which means: come to the reason for eternal success in the hereafter. Al-falāḥ in Arabic means eternal and everlasting; consequently, the prayer is called this because it causes the Muslim to reside in Jannah permanently.

Nuʿaym ibn Ziyād Abū Ṭalḥah (رضي الله عنه) reported: “Al-Nuʿmān ibn Bashīr (رضي الله عنه) said: ‘We then prayed qiyām with the Prophet (ﷺ) on the twenty-seventh night until we thought that we would miss falāḥ.’ That is what they would call saḥūr.” (Reported by al-Nasāʾī, and Shaykh al-Albānī authenticated it.)

Therefore, saḥūr is also called falāḥ because it causes the fasting person to remain strong and energetic throughout his entire fast which is a relatively long time.

Al-falāḥ means to remain, and saḥūr is called this because it causes the fasting person to remain strong and energetic while fasting. Conversely, whoever does not have it is [usually] weak and lazy, so he jeopardises his health.