Puranas mention that one Deva day (day and night) is one year on the mortal world. What does this actually mean?
Does this mean that time itself slows as a result of various (unknown) factors by applying Einstein's theory of relativity or does it mean devas to spend 360 human days (in terms of real time, just like humans spend here) to complete one of their day?
Is there any scripture that helps us better understand this relationship?
Yes, Deva's 1 full day typically means, 1 full year of humans. However it's not strictly applicable for all Deva. Depending on lower to higher plane of existence, it decreases or increases.
From this answer you may find its scripture backup:
The sun makes the day and the night for the world of man. The night is for the sleep of all living creatures, and the day is for the doing of action. A month of human beings is equal to a day and night of the Pitris. That division (as regards the Pitris) consists in this: the lighted fortnight (of men) is their day which is for the doing of acts; and the dark fortnight is their night for sleep. A year (of human beings) is equal to a day and night of the gods. The division (as regards the gods) consists in this: the half year for which the sun travels from the vernal to the autumnal equinox is the day of the deities, and the half year for which the sun travels from the latter to the former is their night.
To understand this time multiplier, we have to understand "who are deva?". In popular culture, these deities are depicted as some human like beings who are floating in cloudy skies with royal cloths. But that's just symbolic.
The real meaning as following:
Usually all the natural elements are with divine qualities like Air, Water, Fire, Land & many many more. For them there is an assigned symbolic deity as VAyu, Varuna, Agni, Bhoomi. Even seasons (Ritu), passion (KAmadeva), humanity, earth, Sun... All have their own deities.
Day = Cycle (not perfectly repeating)
Now how humans repeat their routine in daily basis (wakeup, freshen, eat, work, rest, socialise, sleep); these above elements also have their own routines which they fulfill on their own daily basis. The difference is that, their cycles are quite longer compared to humans days.
An easy example is Earth (Bhoomi devi). It takes 1 year to finish set of events for earth. After that all events again take place with slight changes. From Earth perspective it has finished 1 cycle or its 1 day. But humans feel that 1 year is passed.
Think like this: A mosquito finishes its full life, which humans feel just like a week. Certain bacteria feels like millions of lifetimes just for 1 human day.
Higher the plane a deity resides, longer the human duration. A Sun's day is even longer that Earth's day.
The topmost deva is Brahman, whose every day perfectly repeats. But for humans it feels like several era-s.
Devas are beings who generate, emit their own light (at Cosmic level, stars do that by nuclear fusion) Brahmins, as well as purest neotenic slim beautiful shiny slim faced caucassians, East asians are sattvic in nature, devas, as well as we are descended directly from saptarishis and vedic gods when indra had his palace at North pole, pure souls get born to pure light families based on nature of subtle body, before all gods left earth, as well as North pole aryan divine homeland, when Kali Yuga started, and most purest souls who're turiya from birth, beautiful slimmest faced East Asian females are apsaras, we're ruled by soma in our head. In lower Chakras materialistic obsessive nature, time moves, aging is fast, as well as physical appearance is very ugly, unsightly, eyesore, disgusting to look at, as well as wider, larger skull with smaller brain, huge facial structures, more dark or ugly unnatural proportion, symmetry, faced, bodied one is, more tamasic they're, nature of subtle body gives rise to physical bodies, as well as reveals, hints about true nature, aging, in higher Chakras, as well as planes, dimensions of existence, time moves slow or even freeze (in case of Samadhi, Yoga nidra) relative to subject, as well as longevity of life. Lowest planes of existence (africans, Dalits, Shudras are tamasic, as well as most demonic souls, with infinite sins, that's why divine is never on their side, human body is abode of all deities, everything we offer to our body, affects our subtle bodies, as well as our body, not only food, drink, but thoughts, see, hear, etc, when deities are not pleased and instead angered continously, wrath, infinite suffering, karma sins, ensues) have very shorter lives, diseases, suffering, all negativity, without any 'human' western scientific' intervention which includes' Allopathy' which is same as evil ravana forcibly freeing sinners from wrath, clutches of Yama, against the divine laws of Cosmos, creation.
