Your details stay on this device. The signature is built in your browser and nothing is uploaded.
Adding it to your mail app
Press Copy signature, then open your mail app’s signature settings and paste. In Gmail that is Settings, See all settings, General, Signature. In Outlook on the web it is Settings, Mail, Compose and reply. In Apple Mail it is Settings, Signatures. Some apps, such as Thunderbird, take the HTML code instead.
Why a table?
Mail apps handle modern web layouts poorly, so the signature uses a simple table with the styles written on each part. That keeps it looking the same in most inboxes, on phones too. The plain-text version is for apps and replies that do not show formatting.
Your logo
The logo is placed inside the signature itself, so there is nothing to host. Some mail apps hide pictures placed this way; if yours does, leave the logo out and the rest of the signature still works.