When trying to use Mac Mail on my Apple iMac to check my ISPs email a message appears saying that my password is incorrect. I have verified the password with my ISP but it still does not work.

The message that appears in email clients when your password is rejected can be misleading, as sometimes it is an incorrect username rather than an incorrect password that is the root cause of the issue. In general, mail servers (and most servers) will accept any username (valid or not) and then request a password. Only after a password has been entered will the server attempt to authenticate the username and password combination. This means that if your username has been entered incorrectly then the server will attempt to validate the combination of username and password, which will be rejected, and the reason given is an incorrect password. Strictly speaking, the error about the incorrect password is also true (since you have entered an incorrect password for that username) but it would be useful if the message also indicated that the username was not correct. The reason that most servers do not notify when the username is incorrect is for security reasons, as if someone is trying to brute-force their way into an account on the server (try a list of common usernames and passwords until a valid combination is found) then they need to know two pieces of information – the username and the password. If a message appeared when the username was incorrect then the malicious hacker attempting to gain access could first try a range of potential usernames until a valid username is found, and then attempt to brute-force the password. Whereas, if no notification is given about whether a username or valid or not, they do not know whether a particular username is valid or not.

Since you have verified that your password is correct with the ISP, and you are presumably entering the password correctly into Mac Mail, then the most likely cause of the problem is an incorrect username. This is a relatively common issue (one which I have encountered myself) as some ISPs require you to enter the full email address as the username, whereas others only require you to enter your username. Looking at the website for your ISP there are instructions for setting up email. The instructions state that the username for email needs to be your full email address. You should also verify that you have setup the correct email server addresses, because if you are connecting to the wrong email server that could also explain why the username and password combination is not working.