The help documentation covers these elements, but here's a brief overview:

apex:actionFunction

Provides a function in JavaScript that will invoke the named controller function. You can use apex:param to provide parameters to the function.

 

apex:actionPoller

Provides a periodic timeout function that can refresh the page and call a function. You can emulate the same thing in JavaScript using setInterval and apex:actionFunction; this is a convenience function for that common design pattern.

 

apex:actionRegion

Provides an AJAX action region that will update only part of the page. By default, the entire form that contains an actionFunction, actionPoller, or actionSupport function is updated. You can use a region to isolate part of the form to update instead of the entire form, resulting in faster function calls and avoiding undesirable validations or other side effects.

 

apex:actionStatus

Provides a region where you can display a "working" notification so that the user is aware that a server call is being invoked. This can be valuable during long calls so that users do not perform multiple actions that might affect each other.

 

apex:actionSupport

Provides built-in event support for a given element. You can emulate this feature using JavaScript and actionFunction functions. This element automatically provides the correct support for the element in a cross-browser compatible fashion. The most common use of an actionSupport appears to be to perform a page update when an input field is modified, but it is certainly possible to provide other types of updates, such as clicking on a piece of text.