IIS web sites run under application pools and if you look under "Advanced settings" you see an application pool runs under an Identity.
This Identity can be a number of accounts e.g. ApplicationPoolIdentity or NetworkService. But you can also set your own service account under "Custom account".
I needed to do this but kept getting:
"The specified password is invalid.Type a new password."
Had a conversation with Mr. Google. Seriously - about the only probable cause not mentioned was the proverbial kitchen sink!
Then I realised that this was a domain account so I needed to type:
Bang! Problem solved - sometimes we keep getting confused by all the trees.