Secure Empty Trash overwrites the file(s), whereas Empty Trash just removes the entries in the filesystem so that they are no longer found by the system and may eventually be overwritten. The conventional Empty Trash is what allows some programs to try to recover deleted files, since they are not actually deleted in the strictest sense. Secure Empty Trash is powered by Unix tool srm. You can get some details about it from
this MacOSXHints page or by opening the Terminal and typing the command man srm. It seems that a normal srm or Secure Empty Trash command applies a 35-pass Gutmann algorithm, which I assume means overwriting the file 35 times with random values.
If you just want to get rid of what's in the trash, you should just use the normal Empty Trash. If, on the other hand, there's sensitive data you don't want anyone (including you) to ever be able to recover, use Secure Empty Trash.