Software piracy is when people illegally copy and distribute pieces of software. The term is usually meant to refer to the illegal copying of computer programs.
The illegal copying of programs is a huge problem for the computer software industry. Companies like Microsoft are very concerned about it. For example, I have read that over 90% of computers in China that are running the Windows operating system have illegally pirated copies of that program. This clearly is a huge loss of potential income for Microsoft.
You can also see how worried they are about it by looking at all the programs they try to get you to use that will tell them whether your Microsoft programs are legitimately yours or whether they are pirated.