How can a contact force have both a normal component and a frictional component? What does it mean? My syllabus says that I must understand (and be able to use) the fact that:

a contact force between two surfaces can be represented by two
components, the normal component and the frictional component

What does this mean? I have been trying to understand this, and I tried to think of a few contact forces -- friction, tension, air resistance. I don't understand how friction, for example, could have both a normal component and a frictional component.
Similarly, what if the surface is smooth and there is no friction? How, then, can some force have a frictional component?
Those of you out there that understand physics/mechanics can probably see major gaps in my understanding. I cannot know because I do not even know enough to know.
My textbook does not clarify this, and I am an almost exclusively self-taught high school student (with no peers/teachers whatsoever). Therefore, I would appreciate a thorough explanation.
Thank you!
 A: 
I don't understand how friction, for example, could have both a normal component and a frictional component.

Your syllabus doesn't say this. It says that interaction forces have two components, normal and frictional. It isn't saying friction has these components; friction itself is one of the components.
This is just a general application of breaking forces into components. Of course you can break any vector into components in any direction, but in the case of contact between two surfaces the easiest components are perpendicular and parallel to the surfaces that are in contact. We call the perpendicular component the "normal force" and the parallel component "friction", but at the end of the day its just a single force of interaction between the two surfaces.$^*$ Typically we always break these up right away in physics problems and don't acknowledge that we did, so it is hard to recognize that they are from the same interaction.
Take the example of incline plane problems. We take the gravity force and break it up into components perpendicular to the incline and parallel to the incline. We treat these two components separately even though they come from the same interaction of gravity between the mass on the incline and the Earth. This might have been masked a little bit if instead of showing this derivation we just said "when an object is on an incline there is a 'sliding force' down the incline and a 'pushing force' into the incline."

Similarly, what if the surface is smooth and there is no friction? How, then, can some force have a frictional component?

You can still resolve the surface interaction into normal and frictional components, you just find that the friction component is $0$.

$^*$If you wanted to write out the interaction force, we would just have
$$\mathbf F_\text{interaction}=N\,\hat e_\bot+f\,\hat e_\parallel$$ where $N$ is what we call the "normal force", $f$ is what we call the "friction force", and $\hat e_\bot$ and $\hat e_\parallel$ are unit vectors perpendicular and parallel to the surfaces respectively.
A: The surface needs to support the weight of the body on it and hence exerts a normal.
If the surface is a bit tilted, that is it makes an angle with the ground then it will exert a frictional force on a body lying on it to prevent the body from sliding down.
The two components of the contact force are independent and that is the reason your textbook has mentioned them both separately. To clarify, there is absolutely no friction force acting in the direction perpendicular to a surface; Friction acts opposite to the direction in which the body would slide in.
I'm not very good at English, but I think the idea behind the 'two-component' thing is that in the most general case both friction and normal can exist as a contact force. However, it may be that just one of them is present at a time in a particular case. If a body is at rest with no external forces acting on it then only a normal force acts due to the contact between two bodies.
