Hailullah means: performing the Fajr prayer or staying asleep even after sunrise. This sleep is called "Hailullah" in Arabic because it acts as a barrier between you and your sustenance.
This is the time of raining and distribution of sustenance from Allah.
It is in Jami-Tirmidhi that the Holy Prophet (peace and blessings of Allah be upon him) prayed for blessings in the morning for his Ummah with these words:
Hazrat Fatima (RA) was resting at that time, the Prophet (PBUH) came and addressed her and said:
My daughter! Arise, seek sustenance from your Allah! Be not of the heedless. Allah distributes sustenance to his servants from dawn to sunrise.
Qailulah means resting for some time after or before the Zuhr prayer. It is also a Sunnah along with the habit of the Prophet (peace and blessings of Allah be upon him) and one of the health precautions.
Imam Bayhaqi, may Allah have mercy on him, has brought a hadith in Shub al-Iman that
By sleeping during the day, get the power of worship at night. On Friday, eating and resting after the Friday prayer has been the Sunnah of you and your Companions. As narrated by Imam Bukhari:
The meaning of Ailullah is to lie down for rest after Asr prayer.
It causes respiratory ailments and chest tightness.
According to the opinion of the doctors, sightseeing and light activities should be done at this time. Also, the time for remembrance, thought and prayer has also been mentioned. According to the hadith, this is the gathering of both types of angels, i.e. the angels of the night come and the angels of the day depart.
(Bukhari and Muslim).
Al Haasil
We should organize our schedule in such a way that all matters including eating, drinking, sleeping, waking up, socializing and using social media are disciplined.
@hafizaftab