The spell-checker sends the text to a server, supplied by one of the SPIP user community members, to compare the words with those in a dictionary. The server returns the list of words that are not recognised.
You will then see a new window which contains the article’s text and a box on the right.
Within the text, the words highlighted in red are those that have not been recognised by the server. (If you add them to the local dictionary, then they will be highlighted in green.)
The right-hand box displays all of the text’s unrecognised words in a menu. When you select one of them, a list of possible corrections is offered. You may, if you wish, add that word to the local dictionary instead.
All that’s left, then, is to click in the original window on "Modify this article" and go and correct the words indicated by the spell-checker.