Below the edit box is a Show preview button. Pressing this will show you what the article will look like without actually implementing your edits (i.e. publishing your changes online.) It is strongly recommended that you use this before hitting Publish changes, which will cause your edits to be published onto the page and made visible immediately to everybody.
Use preview during editing to check what the page will look like once they've been saved (i.e. published online) and to check that you haven't made any errors. It also prevents the need for multiple 'publish changes'. Publishing the same article several times in quick succession makes it harder for people to check what changed, and clogs up the
Tip: When you preview, you will also see a preview of the edit summary, so e.g. links can be checked.