For me and you, let's just say that macro photography can be defined as taking close-up photos and that's it's a ton of fun!
The diagram below show that the actual spider is two inches big and the size of the spider's image on the sensor is only 1 inch. Technically speaking, this is not true macro photography. Being more practical, I say that we can call it macro photography because it's very close-up/
Some people, when asked what is macro photography, would say that the magnification factor absolutely must be 1:1 (one to one) or larger. That is the size of the image of the subject on the sensor must exactly the same size as the subject or even larger than the subject to be defined as macro photography.
Although the spider above would definitively be quite a close-up photo, it is only a 1:2 subject to image ratio and would not qualify as macro photography under the stricter definitions of macro.
The official definition of a macro lens is a lens that should be able to produce a life-sized image of the subject directly on your digital camera's sensor. A genuine macro lens will give you a 1:1 subject-to-image size ratio, or in other words a magnification of at least 1.0.
Usually macro photography lenses are needed to achieve that 1:1 magnification ratio. There are other options available to get close-up photography accomplished. You can attach a tele-converter to your lens to increase magnification without having to move farther back from your subject.
Tele-converters go between the camera body and the lens but do not let you get any closer to your subject which is one of the key aspects needed to take good macro images.
You can also use extension tubes that also go between your regular or macro lens to give you the ability to get closer to your subject. They increase the distance between you lens and camera so that you can decrease the distance between your lens and subject.
A more enticing description of what macro photography is that it's an absorbing activity that will let you visually enter into close places and take a photo that will reveal a new world within that is not available to us with the naked eye.
Most compact digital cameras and DSLRs now have a macro mode. I am dating myself here but "when I was a kid" I used screw-on diopter filters or professional lens bellows to shoot macro photos.
Whatever definition of macro photography you use, have a blast! Make it Fun! Go ahead, what are you waiting for?
Shoot more photos. Shoot better photos.