Newton's laws of motion define force based on facts and experiments. Our basic understanding of force is what our common sense tells us about forces. Push and pull are the forces to our common sense. Of course they are forces but defining force based on common sense only is not a good idea.
For example, the gravitational force is pulling us and we don't even know something is pulling us and normal force is also pushing us resulting zero net force, so we can stay still in our place. It is very common to us and we neglect it entirely and we think there is no force at all. When we push or pull something, then we call it force.
So, just the basic understanding as the push or pull is not sufficient (indeed push and pull are forces - your basic understanding is not wrong but not just sufficient enough to define force). The basic understanding sometimes makes the very simple Newton's laws hard to grasp. So be careful!
Force refers to an interaction to a body by means of another body or between a body and its environment.
Force is an interaction, that is not just a single body is involved in force but a result of mutual involvement two bodies (you'll be clear more on this in Newton's third law) exerting and experiencing force. You'll understand in Newton's third law that forces always come in pairs. We'll define force again using Newton's first law.
When you kick a ball, you exert force on the ball and you do that with physical contact with the ball. The forces with physical contact are called contact forces. Tension, normal and friction forces are the examples of contact forces.
Another kind of forces are field forces where the interaction takes place in empty space without touching or physical contact such as gravitational force. Another example is the force between two magnets.
All fundamental forces of nature are field forces which are gravitational interactions (between bodies), electromagnetic interactions (between electric charges), strong interactions (between nuclear particles), weak interactions (in certain radioactive decay process).
Superposition of Forces and Net Force
A force is an interaction. If you apply a force on a body, the body is not only playing a role here, you are also involved applying the force. The body gets a force and you apply it. So the mutual interaction between bodies or a body and its environment is called force.
If a body has been applied multiple forces, the resultant or net force on the body is the vector sum of all individual forces. Since force is a vector quantity which is always associated with a direction (if you are applying a force, you must first know in which direction you are applying the force), the sum must be the vector sum.
A net force is the vector sum of all forces (interactions) on a body. If the net force is not zero, the motion of a body must change.
If $\vec F_1$, $\vec F_2$ and $\vec F_3$ are acting on a body, the net force due to all individual forces acting on the body $\sum \vec F$ is
\[\sum \vec F = \vec F_1+ \vec F_2 + \vec F_3\]
The resultant force, unbalanced force and total force all mean the net force. We make sure that a body is acted on by no net force in Newton's first law of motion. If you are to understand Newton's laws of motion (especially Newton's first law), you must understand what inertia is.