Script Doesnt Change :GetChildren() Parents?

Expanding on Kingu_Criminal's answer.

As Kingu_Criminal said, the GetChildren method returns an array. In the script you provided, you attempt to modify the table rather than the objects inside it. You must index the array with a number to get the value from the table.

For example

local Table = {"apple", 1}

print(Table) -- would print the actual table object

print(Table[1]) -- is indexing the first element of the table, which would be "apple"
print(Table[2]) -- is indexing the second element of the table, which is the number 1

Just like Kingu_Criminal said, you can use a for loop to iterate over the table

local Table = {"apple", 1, 8, true, false}

local currentIteration = 1
for index, value in ipairs(Table) do
	print("Iteration #"..currentIteration.." = Index Position:", index.." | " .."Value:", value)
	currentIteration += 1	
end

Output = [[
Iteration #1 = Index Position: 1 | Value: apple
Iteration #2 = Index Position: 2 | Value: 1
Iteration #3 = Index Position: 3 | Value: 8
Iteration #4 = Index Position: 4 | Value: true
Iteration #5 = Index Position: 5 | Value: false
]]

The for loop will iterate over the array and return the index position and the value for the current iteration.

local Lighting = game:GetService("Lighting")
local ReplicatedStorage = game:GetService("ReplicatedStorage")
local daySettings = ReplicatedStorage.Daytime:GetChildren()
local nightSettings = ReplicatedStorage.Nighttime:GetChildren()
local LightingChildren = game:GetService("Lighting"):GetChildren()

local function setParent(children, parent) -- Using a function is just for convenience so you wouldn't have to use multiple for loops to do the same thing.
	for _, child in ipairs(children) do -- The underscore means we won't be using the index position.
		child.Parent = parent
	end
end

while true do

	setParent(LightingChildren, ReplicatedStorage.Nighttime)
	setParent(daySettings, Lighting)

	script.Day:Play()
	task.wait(378.346)
	script.Day:Stop()
	task.wait(1)

	setParent(LightingChildren, ReplicatedStorage.Daytime)
	setParent(nightSettings, Lighting)

	script.Night:Play()
	task.wait(257.291)
	script.Night:Stop()
	task.wait(1)
end

Let me know if you need any further assistance.