From Ajax Patterns
Asynchronous: Ajax applications generally use asycnhronous (or "non-blocking") calls to the server. When a call is made, a callback method is specified. Normal interaction then continues, and the callback method should soon be called and provided with the server's response.
AJAX: A term sometimes used in place of "Ajax". AjaxPatterns.org now uses "Ajax" exclusively, because, despite its origins as an acronym, "Ajax" is easier to say, looks cooler, and was in any event the form used right when the term was coined.
Design Pattern: See Pattern.
DHTML: Dynamic HTML. Modern browsers allow objects to register as event listeners on most page elements, e.g. an spell checker can be registered to receive changes that occur on a textarea.
Pattern: A form of knowledge reuse. People solving the same problem often end up with similar solutions. A pattern gives a single name to all these solution and summarises the general ideas behind them.