Mailing lists are services where email messages sent to the list are forwarded to everyone that is subscribed to the list. By subscribing to a mailing list you are able to have discussions with a wide number of people on various topics. You can also just sit back and read what other people have posted. The advantage of a mailing list is that they tend to have fewer posts than newsgroups do along with a narrower focus and more specific topics. This means that you don't need to wade through numerous posts that you don't care about.
Mailing lists are also able to focus in on fairly specific topics.
If, for example, you are only interested in discussions about Mormon history you can pick a list where feminism and politics aren't discussed. The disadvantage of mailing lists is that they can be slightly complicated to use. Busy lists can also fill up your mailbox. These usually aren't big problems though. If you read and delete your mail regularly, then your mailbox shouldn't fill up.