These are rules that are triggered and evaluated on certain events as described in the Introduction. They let you define conditionally executed actions based on occurring events (ECA-rules).
Input evaluators allow you to dynamically build texts or numbers at rule evaluation time. Examples of input evaluators are token replacements (from the Token module), or the PHP input evaluator. Input evaluators can make use of all available variables in scope at the time they are invoked. For example, when a comment is being viewed, the comment, the comment's content, the viewing user, the comments author, and so forth, are all available to the input evaluator to build texts or numbers for use in the action or condition.
Actions and conditions specify for which input fields you may use the input evaluators. This allows you to plug in an input evaluator by installing the Token module and to use it in every action / condition. To get the PHP input evaluator, you need to have drupal's PHP input filter module (ships with drupal core) activated.
Rule sets are similar in concept to subroutines and can be invoked by actions or another module. A rule set always works upon some specified arguments, with which its rules operate. So it's useful to create a rule set for some common tasks and to invoke it (by action) out of triggered rules when needed.
Example given: You want to log some user actions on a site. So you create a rule set, which takes the log message and its user and logs it, but only if the user has not disabled it. So you can invoke this rule set from multiple Triggered Rules, without the need of configuring the same condition again and again.
Other modules can provide further features, for example Rules itself ships with two submodules: Rules Scheduler (to schedule execution of rule sets) and Rules Forms support (to apply rules to the Drupal form API). See the Useful modules section for more information.