Why use Mailman
Do I need a mailing list?
If you have a number of people you'd like to send email to as a group, do you need to set up a mailing list? Not necessarily. You may just have an alias in your email client that sends to a group of people, or you can ask your email hosting provider to set up an email alias that contains a list of people.
If your list of people changes often, if it's a large list, if you sometimes have email addresses that bounce, or if you what to keep an online archive of email messages you probably want a mailing list.
What is Mailman, what does it do well?
It's mailing list server with a web based interface. It handles automatic bounce processing, content filtering, archiving, digest delivery, spam filters and more. It's great for discussion lists, and for deciminating information to a group of people. It's text oriented. You can attach pictures and documents, but it's not great at sending a templated, glossy newsletter type of email message.
Bounce processing
One of the more difficult things to deal with when managing a mailing list is when a message doesn't get to the subscriber. This may be a temporary problem, like their mail server was down, or a more permanent problem like they changed email addresses and didn't tell you. Receiving a ton of bounce messages isn't fun. MM takes care of this and there are many knobs in the configuration for you to tell it exactly what to do. It's default behaviour is pretty trouble free.