Web Enumeration is useful to find public resources, incorrectly hidden information, and general information about the target.
Active enumeration involves scanning things, like ports, services, networks, and websites. Passive enumeration uses search engines, WHOIS lookups, DNS, and other analysis.
Tools
While curl and nmap can provide a lot of information, a few other tools can help more. Nikto is a general powerful website scanner. WafW00f can check for Web Application Firewalls (WAF).
The entire process can be automated with tools like FinalRecon, Recon-ng, theHarvester, SpiderFoot, and the OSINT Framework.