The web first started as static HTML pages. Later dynamic web pages were introduced putting life into the web by interacting with databases and the user. Those dynamic web pages collectively enabled web developers to develop web applications using a server side scripting language of their choice such as Perl, PHP, ASP, JSP, Python among several others.
The problem with web applications was that compared to regular desktop applications they were pretty much slow in response time. An attempt to answer this issue came from Sun by introducing and strongly pushing Java Applets as the way ahead to create dynamic rich web applications that were responsive much the same as their desktop counterparts.
The problem with Java Applets was that they were heavy to load, not to mention you had to have the JVM installed on your machine. Microsoft, being an opponent of Java due to its threat on Microsoft's operating system and office monopoly, tried to push Flash forward as an alternative for Java Applets. Indeed Microsoft managed to throw Java Applets from their hoped for place and position Flash instead. First Flash was touted as the means to do animation for the web, which was also what Sun was pushing Java Applets to be, a way of making rich graphics and animation on the web, later Flash was pushed further and proposed as a method for making rich web clients that are interactive with users much the same as web applications, Java Applets tried to do so as well but failed.
Enter AJAX. AJAX appears to be the answer for what Flash and Java Applets failed to achieve. Indeed Google is pushing AJAX forward and using it in many of its applications such as Gmail, Google Calendar, Google Docs & Spreadsheets, Google Maps and many others.