Goal
We have multiple ways to acquire digital images from the real world: digital cameras, scanners, computed tomography, and magnetic resonance imaging to name a few. In every case what we (humans) see are images. However, when transforming this to our digital devices what we record are numerical values for each of the points of the image.

For example in the above image you can see that the mirror of the car is nothing more than a matrix containing all the intensity values of the pixel points. How we get and store the pixels values may vary according to our needs, but in the end all images inside a computer world may be reduced to numerical matrices and other information describing the matrix itself. OpenCV is a computer vision library whose main focus is to process and manipulate this information. Therefore, the first thing you need to be familiar with is how OpenCV stores and handles images.
Mat
OpenCV has been around since 2001. In those days the library was built around a C interface and to store the image in the memory they used a C structure called IplImage. This is the one you'll see in most of the older tutorials and educational materials. The problem with this is that it brings to the table all the minuses of the C language. The biggest issue is the manual memory management. It builds on the assumption that the user is responsible for taking care of memory allocation and deallocation. While this is not a problem with smaller programs, once your code base grows it will be more of a struggle to handle all this rather than focusing on solving your development goal.
Luckily C++ came around and introduced the concept of classes making easier for the user through automatic memory management (more or less). The good news is that C++ is fully compatible with C so no compatibility issues can arise from making the change. Therefore, OpenCV 2.0 introduced a new C++ interface which offered a new way of doing things which means you do not need to fiddle with memory management, making your code concise (less to write, to achieve more). The main downside of the C++ interface is that many embedded development systems at the moment support only C. Therefore, unless you are targeting embedded platforms, there's no point to using the old methods (unless you're a masochist programmer and you're asking for trouble).
