The & symbol is used to denote that the following argument should be treated as the block given to the method. That means that if it’s not a Proc object yet, its to_proc method will be called to transform it into one.
Thus, your example results in something like
Post.all.map(&:id.to_proc)
which in turn is equivalent to
Post.all.map { |x| x.id }
So it iterates over the collection returned by Post.all and builds up an array with the result of the id method called on every item.
This works because Symbol#to_proc creates a Proc that takes an object and calls the method with the name of the symbol on it. It’s mainly used for convenience, to save some typing.