Hardware refers to the physical components of the computer that run the software; such as the hard drive, the motherboard, the video and sound cards, the monitor, the printer, the keyboard and the mouse. Hardware also includes removable storage devices such as a CD Rom Drive or Zip Drive.
Software refers to things that are used by the hardware, such as programs that you install on your computer including games, word processing programs, spreadsheet programs, graphic design programs and the like.
There is an in between category called firmware or middleware. This is the program initially installed on your computer that allows you to run all other programs. Examples include operating systems include MS Windows, Linux and Mac OS. Basically, firmware is the go between the software and the hardware; translating the software into a language that the computer can understand and respond to.