What is the "APM, Web Application" module used for?

A web application means you can have a application that is configured in LTM and you can put an authentication front end on it using APM. This is called APM+LTM mode. It means you can add authentication using AD, LDAP, Certificate, Tacacs, Radius, Kerberos, NTLM, etc including 2FA to the authentication for that application. Then you can pass the relevant bits to the application so it logs in automatically using the credentials supplied to APM by the user.