Newsgroups (or Usenet - the collective name for newsgroups) are basically discussion groups conducted on the Internet. There are groups for just about every interest (examples include comp.sys.amiga.misc, alt.dreams.lucid, alt.books.poppy-z-brite, and so on). A newsserver is a server which contains the data for these newsgroups, and you connect to one of these in order to download messages for newsgroups that you have specified (you are said to be 'subscribed' to these newsgroups). Newsservers exchange data, so if you post a message to a newsgroup (more on that later), it will be copied to all other newsservers that host that newsgroup. Note that not all newsservers carry information of all newsgroups, but a typical newsserver will have at least 30,000 groups, some are in the region of 60,000. It is possible to download a list of available newsgroups on your newsserver (but you don't have to do this if you know the newsgroup name, and are willing to assume it is on your newsserver).
NewsCoaster is can now either read offline or online. Offline means it connects to your newsserver and downloads news to your machine, for you to read later at your leisure. Online reading lets you browse through the articles whilst online, which is generally more costly for those paying 'phone bills, but means your hard disk is filled with only the messages you choose to read, and is generally better for those with free connections. You can specifiy online or offline reading for each newsgroup individually.
Please note that NewsCoaster's online reading is current experimental, and may contain bugs. Originally NewsCoaster was an offline-only newsreader, and this is the most tested feature.
When NewsCoaster downloads news from a newsgroup for a first time, it will download a certain number of the most recent ones. From then on, it will either download all the messages since you last downloaded, or alternatively you can set a maximum number of messages to download. As well as reading messages, you may write some yourself - this is referred to as 'posting' to that newsgroup. It is possible to post to more than one newsgroup (known as 'crossposting') - although this is generally discouraged.
For every newsgroup you wish to read, you create a 'new newsgroup' for it in NewsCoaster - this means a folder on your hard disk is created for storing news items locally, and an entry appears for it in the window. You don't have to download news for a particular newsgroup everytime you go online - you can temporarily 'unsubscribe', which means the messages you have already downloaded are not deleted and can still be read, but new news won't be downloaded when you 'fetch news'.
Lastly, if you are new to usenet, you should at some point look at the netiquette section, which describes what is considered 'acceptable' behaviour on usenet. Read it if you don't want to upset people!