Here are the explanations for the “min, desired and max” values from AWS support:
MIN: This will be the minimum number of instances that can run in your
auto scale group. If your scale down CloudWatch alarm is triggered,
your auto scale group will never terminate instances below this number
DESIRED: If you trip a CloudWatch alarm for a scale up event, then it
will notify the auto scaler to change it’s desired to a specified
higher amount and the auto scaler will start an instance/s to meet
that number. If you trip a CloudWatch alarm to scale down, then it
will change the auto scaler desired to a specified lower number and
the auto scaler will terminate instance/s to get to that number.
MAX: This will be the maximum number of instances that you can run in
your auto scale group. If your scale up CloudWatch alarm stays
triggered, your auto scale group will never create instances more than
the maximum amount specified.