Macro

According to wikipedia the definition of Macro Photography, is extreme close-up photography, usually of very small subjects, in which the size of the subject in the photograph is greater than life size.

The more common usage is any close-up photography where you can see the details of your subject in a much more intimate way than you would with the naked eye.

Another definition of the term macro photography is extreme close-up photography in which the image on the film is as large as, or larger than, the object.  Often the amount of closeness is expressed as a magnification factor such as 1:1.

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.

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 your lens and camera so that you can decrease the distance between your lens and subject.

Another 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.

Whatever definition of macro photography you use, have a blast!   Make it Fun!  Go ahead, what are you waiting for?
Links:
http://monicaroyal.com
http://photography.tutsplus.com/articles/130-stunning-examples-of-macro-photography--photo-1717
http://www.smashingmagazine.com/2008/09/21/25-beautiful-macro-photography-shots-photos/