1Password does two basic things: it manages your passwords and it secures them in an encrypted vault. So there is a degree of security provided, even for simple passwords. And there is certainly a convenience factor provided for both long and random or short and non-random password management.
The most secure way manage passwords is to allow 1Password to generate long randomized passwords, but it is entirely possible to use your own passwords within the 1Password app.
For sensitive web sites such as bank accounts and email account access, you should use long, random passwords, unique for each account. For non-sensitive accounts such as discussion forums, simple passwords should be OK, as long as you use different password for each site. 1Password doesn't really care what type of password you use - it handles short, non-random passwords and long, randomly-generated passwords equally well.
You would absolutely NOT want to use your "master" 1Password password to access web sites. That master password should only be used so that the 1Password app can access your encrypted, locally-stored password vault.
