If you don't check, you don't know what is posted. When using a mailing list, you use your regular email software and anything posted to the list is automatically forwarded to you. This is why some people refer to the list server as mail exploder. A person sends a message to the list's address and the server automatically sends it to all people on the subscription list. In order to distinguish between email sent to individuals and to the list, we talk about posting to the list, in parallel to posting something to a bulletin board on the corridor.
Posting is really a synonym for emailing.
Posting is done by sending email to list's address. Replying directly to the poster is often referred to as taking the discussion off the list. This serves as a reminder and puts the reply in context. However, do not overdo and quote too much. Users that subscribe to a digest and include the entire issue quoted in a reply to a single post are not winning any cheers.