The only model I'm familiar with is diffuse lighting but this look way more complicated than that.
4 Answers
Each square has a light level from 15 to 0. Each level is 20% less than the level above it. If a square contains a light source it gets the luminosity of that light source, otherwise it gets one less than the brightest neighbor.
Sunlight is special, it suffers no vertical attenuation.

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3Just a thought, would adjacent blocks (blocks connected by a corner) be considered neighbors with this algorithm? – Jess May 31 '11 at 23:45
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@Ben No diagonal blocks are not neighbors in this calculation. – Bradley A. Tetreault Jul 03 '14 at 17:59
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Are you sure that Minecraft has nothing to do with deferred shading? – McLovin Nov 05 '15 at 19:23
While the answer by Loren is mostly correct, I’d like to add that the minecraftwiki has further information.
Sunlight and moonlight works by essentially making blocks with nothing but air and glass above glow with the current lightness (15 at day, 7 at night and something between at dusk/dawn)
The falloff described by Loren means that level 0 still has 0.8¹⁵·100% = 3.5% lightness (to quote my own edit in the minecraftwiki)
The smooth lighting intruduced with Beta 1.3 works by using the light values of the adjacent blocks to generate a gradient.

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I assume smooth lighting works by taking the adjacent blocks *for each corner*. – eap314 Mar 25 '22 at 11:12
The light sources in Minecraft are as listed: Of course, sunlight during a thunderstorm and the nether's light are exceptions to the rule: If the light level is UNDER 7, entities will spawn. These are both over 7, but mobs will spawn because in the nether, it acts as if it is night, and because a thunderstorm changes the "time" of the day, mobs do spawn.
Beacon 15
End Portal Block 15
Fire 15
Glowstone 15
Jack o'Lantern 15
Lava 15
Redstone Lamp, when powered 15
Sea Lantern 15
Torch 14
Furnace, when active 13
Glowing Obsidian 12
Nether Portal Block 11
Redstone Ore, when touched 9
Ender Chest 7
Redstone Torch, when on 7
Brewing Stand 1
Brown Mushroom 1
Dragon Egg 1
End Portal block 1
Other
Sunlight 15
Sunlight, during Rain or Snowfall 12
Sunlight, during a Thunderstorm 10
Moonlight 4
(Cited from this website: https://minecraft.gamepedia.com/Light#Sources_of_light)

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If you place a light source on a flat dark place, you will get a square of light, turned around by 45°, with the middle in the light source. The size is equal to the middle light value
Natural light values are:
Clear weather: 15
Rain: 12
Rain with thunder: 10
Night: 4
Night with Rain/Thunder: 4
Note that Thunder Rain will behave like if it was night - you can sleep, mobs spawn, etc.
If this Answer scores 1pt. it's a record!

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