This C programming tutorial introduces arrays as a way to store multiple pieces of the same data type within a single variable. The tutorial contrasts this with using numerous individual variables, highlighting arrays' efficiency for tasks like storing the ages of 100 people. The syntax for declaring an array is explained: `data type array_name[array_size]`. The `data type` specifies the type of data (e.g., `int` for integers), `array_name` is the identifier, and `array_size` determines the number of elements. An example shows declaring an integer array to hold the ages of five people.