After the administrator verifies your account, a confirmation email will be sent to you.

Literal

Administrator [by-によって] account [possessive-の] authentication [subject-が] performed-[passive-た] after, you [to-に] confirmation [possessive-の] email [subject-が] sent.

管理人によって 'by the administrator' — によって marks the agent in a passive construction. 認証 'authentication/verification.' 行われた後 'after it is performed.' A standard system notification — formal, impersonal, passive-heavy.