Nasser is incorrect in saying that code in initialization cells are executed on opening the notebook they are in. Upon (manual) evaluation of the first line of code Mathematica offers to evaluate initialization cells first. Only if you agree, and only then, is the initialization code evaluated.

A solution to your problem may be the use of the Manipulation option SaveDefinitions, but you should be aware of the dangers of using it.

You got the order wrong. If you put the Initialization :>... at the end, not first thing, it should work. The Manipulate pattern is this

  Manipulate[   somecode; somecode; morecode; Show[....], 
                        controlVariable,
                        controlVariable, 
                        Initialization :> (...)]

See if it works now.

The cell where points1 is defined, has to be an initialization cell, not just a normal cell. An initialization cell will automatically get evaluated when the notebook is loaded. But I would just rewrite your Manipulate by simply putting the points1=... code inside Manipulate itself, so you do not have to worry about all of this. Simply write Manipulate[.....,Initialization :> (points1=Table[...])] and now everything is in one place.

It happens if Dynamic Content for the notebook is enabled, so Manipulate starts working on load to present a picture, but

points1 = Table[<snip>, {i,70},{j,70}]

remains unevaluated, as the error message says. It can be fixed be putting

points1 = Table[<snip>, {i,70},{j,70}]

into a separate Initialization cell or by disabling Dynamic Content, of course.

I tried separating the cells, but I'm still getting errors when first opening the notebook. What did I do wrong? (See image below.)