Although cursive has a unified design, everyone writes cursive a little differently. The idea is that cursive is designed to write whole words in a single stroke. The concept of a secure signature in cursive is that the more work a single stroke is, the more uniquely a person writes it.
That is to say, even though you may have the same name as someone else, it’s extremely unlikely that a person can copy your nuances precisely enough to forge your signature on the fly. It isn’t a perfect system, but it’s easy enough to verify a signature that people could do it before technology was around to aid that process.
That concept is also why they say the actual design of your signature is less important than the consistency of doing it the same every time.