I felt that episode two was mostly an informative episode issued to answer the basic questions regarding on what are the Claymores.
The significant topics addressed are the tidbits of Clare's past, which are going to be leaked episode by episode until they give the answer to Laki's question about why Clare became a Claymore to fight Yoma that badly, and finally the pain and toughness Laki and Clare will have to endure for each other knowing the abysmal fate that will eventually befall on Clare.
They even started to make direct references on what the organization does and established other questions.
I think that most of the development that took place on episode was directed at Clare's past.
I may or not be the only who is making the following comparison.
Mr. X in Claymore hardly reminisces to me John Smith from My-Otome.
And the black card is a slight reminiscence to the Schwarz card, which contains the black crystal, also in My-Otome.