Only the 16th generation iPhone, along with the iPhone 15 Pro and iPhone 15 Pro Max, can support Apple Intelligence. As of the time of writing, here’s the full list of supported iPhones:

iPhone 16
iPhone 16 Plus
iPhone 16 Pro
iPhone 16 Pro Max
iPhone 15 Pro
iPhone 15 Pro Max

Unfortunately, the iPhone 15 or iPhone 15 Plus from the previous generation won't work with Apple Intelligence. To use Apple Intelligence, you will need at least one of the iPhone 15 Pro models or newer.
Is your phone on the list?