Memoization is a programming technique to basically "cache" expensive procedures or operations in order to avoid evaluating their results again.

Take this function for example, to generate a character list starting from lowercase chars up to a certain character code:

local mem = {}
function generateCharlist(n)
if mem[n] then
return mem[n]
local str = ''
for i = 97, 97+n do -- start from lowercase
str = str .. string.char(i) -- convert number to character
mem[n] = str
return str
local firstList = generateCharlist(25) -- performs the generation
local secondList = generateCharlist(25) -- uses the pre-generated value
print(firstList, secondList) -- abcdefghijklmnopqrstuvwxyz abcdefghijklmnopqrstuvwxyz

Here once generateCharlist is called the first time, that string is generated and inserted into the mem table, the next time it runs with the exact same param as the first call, it will use the pre-generated value rather than having to spend the time generating it again.

Do not use that code as a good "optimized" example of that process (specifically lines 7-10), since I intended for it to perform poorly. More info about why this is awful to do can be found in the Optimizations page.