Active Record is a "design pattern"—another of those highly abstract systems like MVC, which provide templates for solving common coding problems. In itself, it isn't code, it is just a pattern for code. There are several different interpretations of it. At its core is the creation of a relationship between your database and an object, every time you write a query. Typically, each table is a class (represented by our models), and each single row becomes an object. All the things you might want to do with a table row, for example, create it, read it, update it, or delete it, become "methods", which that object inherits from its class. CakePHP is built around the Active Record pattern, and so is CI—although the exact implementation in the two frameworks seems to have differences.
For example, models in CakePHP are associated to tables, every table has a corresponding model representing it. CodeIgniter gives you a little more freedom here; your models don't need to be associated...