That is an extra fail-safe. In the chance that strarr.each_cons(k).map(&:join).max_by(&:length) returns nil, which it will if the array strarr is empty, then an empty string will be returned. Since nil is falsey, '' (the empty string) will be returned when the || expression is evaluated on the last line—since strings are considered truthy. The first line of the method should handle cases where strarr points to an empty string, but it's not bad to have a back up.

what is the purpose of || "" at the end?

Wow this is amazing

each_cons is so good. but i don't want to using it.

It allows you to pass a method in as a symbol instead of passing in a block to the method itself, which makes it automatically reflexive without any further work. Below would be the longer version of the above example for that part.

.map do |strings|
  strings.join
end

i don't understand anything