How does the code i % 2 == 0 and "Blink" or "Off" work in a script?

I'm assuming you already know how the modulo operator (%) works. In this case, i % 2 == 0 checks if i is even. The code you sent works because Lua uses short circuit evaluation which will be simplified to Lua being short circuited below.

Short circuiting works in Lua by only evaluating the second value if the first value doesn't determine the answer. For example x and y will equal y if x is truthy (a value which is not nil/false) and will equal false if x is falsy (nil/false) because, since x is false, it know that the expression should be falsy as y cannot change the result of the expression if x is falsy. This is also done by or. For example, in x or y, if x is truthy, it equals x and otherwise it equals y

In the code i % 2 == 0 and "Blink" or "Off" will be simplified to x and y or z. The expression mentioned recreates the ternary operator which means that if x is truthy, it equals y, and if not, it equals z. Because of how it exploits Lua's short circuiting, it means that y must be truthy or it will always equal z.

Hope this helps!

local value = i % 2 == 0 and "Blink" or "Off"

it means value = condition and option if condition is true or option of condition is false

it's the same as writing:

if i % 2 == 0 then
    value = "Blink"
else
    value = "Off" 
end

i%2==0 is checking if the number i is even/odd using the modulus operator.

if it is even (i%2 is 0) then set the value to blink, otherwise if it is odd, set the value to off.

The reason the line value = i % 2 == 0 and "Blink" or "Off" works is because of how lua handles truthy values. if i%2==0 is true

there are two things going on here

x = <condition> and <option1> or <option2> is like a shortened if statement

if condition is truthy (aka not nil and not false), then x will be set to option1, otherwise x will be set to option2

another way you could write x = <condition> and <option1> or <option2> would be like this:

if condition then
    x = option1
else
    x = option2
end

so essentially, your code is doing the same thing as this

if i % 2 == 0 then
    value = "Blink"
else
    value = "Off"
end

next, the i % 2 == 0 part

the % operator, or modulus operator, is essentially the same thing as the remainder when you divide numbers

in this case, i % 2 == 0 is used because the remainder of something being divided by 2 will either be 1 or 0

by counting up you get an alternating pattern of 1 and 0, which is useful since the light will turn off every other iteration