Kumo is an assasin of the organization, nicknamed "Arachnid". At the beginning of the series, he received the order to kill Yoshio and Alice. However, noticing her abilities, he instead took her in and trained her to kill, because "it's worth putting her to use" and "he can kill her any time". It was also him who taught Alice to use the Kumoito (lit. Spider's thread).
It is later revealed that the reason he took her in was to kill him, as because of his abilities, no one could kill him. Kumo is not his real name but rather a name given by the organization.