The checks
Every signature the builder shows comes with a proof sheet. Here is exactly what each line tests, so you can judge the result yourself.
Counts the characters of the signature's HTML. Google's Gmail help says: "You can put up to 10,000 characters in your signature." Over 10,000 is marked as a problem. The builder keeps the HTML lean (no icons, no web fonts) so most signatures use 2,000 to 4,000.
Your chosen colour is used for your name and links on a white background. The check computes the contrast ratio with the WCAG 2 formula (relative luminance, (L1 + 0.05) / (L2 + 0.05)). Small text needs at least 4.5 to 1 (WCAG 2 success criterion 1.4.3); below that it is marked as a problem.
When you add a logo address, the check notes that many mail apps hide pictures until the reader allows them, and confirms the logo has alt text (your company name, or your name) so something readable shows in its place. With no logo, nothing waits for "show images".
When you give both, the check compares the domain after the @ in your email address with your website's domain (ignoring "www." and allowing a sub-domain). A difference is a note, not a fault: it is fine if intended.
Each number becomes a tap-to-call link (tel:). A number that does not start with + and a country code is noted, because a phone abroad cannot dial it from the link as written.
Every signature also gets a plain-text version, starting with the standard "-- " separator line, for plain-text mail and phones. The check reports how many lines it has.
Layout tables with inline styles (mail apps ignore most style sheets), common system fonts with safe fallbacks (Arial, Georgia, Verdana, Trebuchet MS, Tahoma), text links instead of icon pictures, and every word you type escaped so it cannot change the markup. Web addresses must start with http or https; profile and logo addresses must be https.