Suppose you decide to post an article telling people of a useful cat thing around the house. You might decide that people would like to read that on rec.pets.cats.misc, also on alt.cats and alt.animals.felines.
If you prepare an article, and send it out three times, once to each group, then people like myself who take each group will download it three times, and come across it three times as an Unread article. Annoying, and an unnecessary cost [outside the USA most of us pay per second of downloading time]. That is multi-posting.
Alternatively, you could send it out once, and in the Newsgroups line you could put:
It will now only be downloaded once [assuming reasonable software]. It will appear in each group, and once it has been read any one group, it will be marked as read in all of them. That is cross-posting.
Cross-posting is often wrong, because people tend to cross-post to unsuitable groups. For example, if your cat has a medical problem, it may be reasonable to cross-post to rec.pets.cats.health+behav and alt.cats and alt.animals.felines because the latter two groups are general cat groups, and someone there may be able to help: but it is not reasonable to cross-post to rec.pets.cats.misc or rec.pets.cats.anecdotes because these groups are for different things. However cross-posting is right some of the time.
Multi-posting is a waste of bandwidth, money, and people's time, with no advantages whatever, and should never be indulged in.
Please, only cross-post if you are sure your article is suitable for the different newsgroups; never multi-post.