Identities are a way for you to send email from different aliases/"profiles." For example, if you have another e-mail address that forwards to your Terabolic account, identities allow you to send e-mail from that address as well using Terabolic.
To add or edit identities, go to "Options" and click the link that reads "Identities / Email Addresses / Signatures." From here, you can add or edit your identity. Please make sure to type in the correct address in the "Your From: address" field.