Force is defined as mass times acceleration. Commonly shown as F = m a. A very simple way to define force is a push or a pull.
Let's look at a simple example of a type of force. A book lying on a table:
Something keeps the book down. Thousands of years ago, there was no name for that force. "Books lie on tables because that's what they do," was the thinking. We now have a more sophisticated understanding of the world. Books lie on tables because gravity pulls them down. We could label this arrow Fg for "force of gravity" or W for it's more common name, weight. Gravity pulls the book down, but it doesn't fall down. Therefore there has to be some force that also pushes the book up. What do we call this force? The "table force"? No that sounds silly and besides, it's not the act of being a table that makes the force. It's some characteristic the table has. Place a book in water or in the air and down it goes. The thing about a table that makes it work is that it's solid. So what do we call this force? The "solid force"? That actually doesn't sound half bad, but it's not the name that's used. Think about it this way. Rest on a table and there's an upward force. Lean against a wall and there's a sideways force. Jump on a trampoline high enough to hit your head on the ceiling and you'll feel a downward force. The direction of the force always seems to be coming out of the solid surface. A direction which is perpendicular to the plane of a surface is said to be normal. The force that a solid surface exerts on anything in the normal direction is called the normal force. Calling a force "normal" may seem a little odd since we generally think of the word normal as meaning ordinary, usual, or expected. If there's a normal force, shoudn't there also be an abnormal force? The origin of the Modern English word normal is the Latin word for a carpenter's square � norma. The word didn't acquire its current meaning until the Nineteenth Century. Normal force is closer to the original meaning of the word normal than normal behavior (behavior at a right angle?), normal use (use only at a right angle?), or normal body temperature (take your temperature at a right angle?). Are we done? Well in terms of identifying forces, yes we are. This is a pretty simple problem. You've got a book, a table, and the earth. The earth exerts a force on the book called gravity or weight. The table exerts a force on the book called normal or the normal force. What else is there? Forces come from the interaction between things. When you run out of things, you run out of forces.