A "program" is a set of instructions for the computer. A program tells the computer how to do something.
Some examples of programs are a game like Solitaire or Hearts, a "word processing" program for doing typing on, a "spreadsheet" program for doing calculations on, a genealogy program for recording and keeping track of your genealogy information, and a "paint" or "drawing" program for drawing pictures on.
"Software" is one or more programs (as opposed to "hardware," which is everything you can touch: the electronic circuits, the keyboard, the screen, etc.). So, software is just another word for programs.
To do anything on a computer, you need a program. To play Solitaire you need a Solitaire program. To do some typing, you need a "word processing" program. (Note: A Solitaire program comes with computers that have Microsoft Windows on them, but it is a separate program.)
To get your computer to do something new, you have to go to the store and buy a new program, to "program" your computer to know how to do the new thing.