Background Info
The protagonist of the series is Alucard, who is immortal, and has a lot of other supernatural abilities, that he can release by the Control Art Restriction System. The smaller levels mean more power. From the level six to the one, he can release the restrictions by his own, but for the zero level, he needs the order of his lord, Integra Hellsing.
When Integra gives the order, Alucard quotes from the Ripley Scroll. As the Bird of Hermes he eats his own wings instead of using his power, that makes him tame. But now, he could get back to his full power.
When the level zero release happens, all the souls in Alucard come out from him and get ready for the battle for him. That is a very big army of lost souls, if we consider how old is Alucard. However, the souls could be killed, just like Alucard in this form, who change back to Vlad Tepes (Drakula).
Moral of the Story
The quote about the Bird of Hermes is an allegory, symbolizing that the hero (call him that way) has decided to restrict himself to protect himself and others. Instead of using freedom, power and knowledge, he has eaten his own wings and limited himself that way.
When he don't want to protect himself anymore, he could only worry for others. Therefore he will never be able to make the decision whereby he grows his wings again. After he gets verification from outer source, that his restrictions no more needed or they make no sense, he could get back to his real nature.
We shouldn't forget that this transformation hides not only strength but weakness, those what he have been protecting himself from. The hero throw down his chains, but he becomes vulnerable at the same time, he will be more human and vincible. The urge what makes him to move somewhere despite this, makes him brave. But if he had become strong enough while he had his restrictions, no simple attacks could hurt him despite these ones reach him more times.
Releasing Control Art Restriction Systems three...two...one, approval of level zero recognized. Commencing the Cromwell invocation. Ability restrictions lifted forever.