Programming is telling a computer how to do something. If you've heard the things you might run on a computer (like games or a Web browser) called "programs," this is why. They are things that were made by programming. Apps on a phone are also programs.
Computers are very good at some things but very bad at others. Programming involves understanding what they are good at. One of the things they are bad at is understanding English and other languages spoken by humans. As a result, when you program, you use a "programming language," which is good at giving instructions in a form a computer can understand. There are many programming languages, each with their own strengths and weaknesses. Professional programmers usually know several and can pick the one best suited to a job.
The world today is incredibly full of computers, and they all were programmed. This website, for example, involves programs that run both on your computer, when you do things like submit a question, and programs that run on computers owned or rented by CareerVillage, which do things like take your question and let me know that you asked it and I might be able to answer. Programs can be very simple, like a classic introduction that just shows the words "Hello world," or very, very complicated, like a famous program called Watson that IBM made which was able to win on the TV show "Jeopardy."
Programming can be very hard and sometimes frustrating, and requires a lot of dedication. However, it also can be incredibly rewarding. If you like it it is a solid career, but beyond that, I find it really fun to be able to make computers do what I want, instead of having to find a program made by someone else.
If you're interested, the website codeacademy.com is a good place to get an introduction.