Network models give you a troubleshooting framework. When something breaks, isolate the problem to a specific layer.
Can't reach a server? Ask: Can I ping it (Layer )? Does DNS resolve (Layer )? Is the cable connected (Layer )? Each question targets a different layer.
Models also enable interoperability. Your browser works with any server because both follow the same protocols. Change your NIC and HTTP still works. Layer changed, but higher layers don't care.