Moodle no longer uses its own spell checker in a text edit window -- like when you post to a forum. Instead, use the spell checker that is built into every current browser (Firefox, Chrome, Internet Explorer, Safari).
Simply CTRL+Right Click (Windows) or CTRL+Click (Mac) on a misspelled word (shows as underlined in red), and the browser's built in spell checker will be activated. Please contact the Help Desk if you have any questions.
Point of clarification on spell check: If you're using Internet Explorer version 9 or below, you will still have the spell checker available in the text edit tools. If the spell checker doesn't appear in the tools (IE 10 and latest versions of other browsers), use the browser spell check method.