The 'solar plexus' is the common name for what might be more properly called the celiac plexus. It isn't just a good spot to hit people, it's also a well-defined anatomical structure, and it's in your body for a good reason. Lets start with a definition:
A plexus is a spot in your body where a bunch of nerves come together, intermingle, and set off in new directions. This is useful because nerves from each part of the spinal cord or brain have specific functions, and any given organ might need to be serviced by multiple nerves. A plexus is where the specialized nerves are split and rebundled for various organs.
The solar plexus is actually a bundle of nerves behind your stomach, where it passes by the celiac artery. It is anterior to the first lumbar vertebra (L1). It is composed of spinal splanchnic nerves that serve the sympathetic nervous system, and part of the Vagus nerve, which serves the parasympathetic nervous system. These nerves recombine into bundles and head off to the lower esophagus, stomach, small intestines, most of the large intestines, liver, pancreas, spleen, adrenal glands, and kidneys.
Being hit in the solar plexus is very painful, and a hard blow can even damage the nerves, which could result in serious organ dysfunction. The solar plexus also serves the diaphragm, and a blow can cause the diaphragm to spasm, knocking the wind out of you and making it difficult to breathe. You can also inject a local anesthetic into the solar plexus, relieving severe organ pain; this is called a celiac plexus block.
While there are numerous plexuses in the body, the solar plexus is notable in that it serves lots of important organs, and of course, in that it is comparatively unprotected. The cardiac plexus, on the other hand, is protected by the rib cage, preventing Jackie Chan from giving the bad guys sudden, violent heart attacks.
It used to be a favorite pastime of anatomists to make up new words for various bodily structures; it is a rare piece of meat that doesn't have at least three different names. The Solar plexus is no exception. I haven't been able to track down who gave it what name when, but here's a quick list of names and what they mean.
'Plexus' is Latin for 'braid', or 'network'.
Solar is Latin for sun, and may refer to the many 'rays' of nerves emanating from the plexus, or it might refer to the central position in the body. This is not actually a very descriptive term, which is probably why it didn't make it into the Nomina Anatomica.
Rarely, you will see the solar plexus called the epigastric plexus. Epi- is Greek for 'beside' or 'over' and gaster is Greek for 'stomach'. This is used in Gray's Anatomy (as is solar plexus), but is rarely seen anywhere else.
The names celiac plexus, coeliac plexus, and plexus celiacus are all based on the Latin coeliacus, meaning 'belly'. Celiac plexus is currently the 'most official' term among medical professionals. So, next time you're watching a ninja movie and you want to show of your cosmopolitan knowledge of anatomy (and Latin!), you can just say "Ha! Got him right in the Belly Braid."