When board powered up led turn on for 1min and meanwhile when button pressed turn off it immediately

The example-code that you posted uses the function millis() for debouncing the button.
This is something different that "waiting for a button-press to switch of an LED"

For the task "waiting for a button-press to switch of an LED" debouncing is not nescessary.

As a pseudo-code

in a arduino-board is powered up the function setup() is executed once

So inside function setup() you code:

switch LED ON

if power is supplied to the arduino-board the function loop() is doing what its name says:

looping infinitely.

So inside loop() you have to do two things
checking if the button is pressed
checking how much time has gone by since powerup

if button is pressed: switch off LED

if one minute has passed by: switch LED off.

The established users just link to this very unsatisfying BWD-example.

Here is a short tutorial that is easier to understand as the "standard" Blink-without-delay-example. (I'd like to call it "blink without explain" )

So please start reading the example-code and then ask specific questions if you do not understand something

best regards Stefan