You may have a better understanding of Quantum Physics after you learn about such concept in college. It is probably not easy to explain in just a few words. Basically you can view the classical mechanics as a derived theory from Quantum Physics when the quantum effects only play a small role. There is a good diagram showing the domains in wiki:

classical mechanics .

Basically in the macroscopic world with relative low velocity, the classical mechanics dominate. But in the microscopic scale, it is where the quantum effects are not negligible.

One key point to differentiate the Classical Mechanics and Quantum Physics is the difference between determinism and probability. In the classical world, you know the past then you know the future. While in the Quantum world, the knowledge of the present will only determine the probability of the state in the future.

There is a simple rule to tell that if you need a plank constant "h" in the formula, then you are in the quantum world; otherwise the classical theory would be fine for description. As for the plank constant h, you may learn it in the future.

Reality deviates from Newtonian physics at all scales. Because the effects of quantum mechanics are most important at small scales, the deviation due to quantum mechanics gets larger the smaller you get, however. Generally speaking, for most physical principles, you need to get on the scale of a nanometer or below for quantum effects to become important. This said, there are visible effects of quantum mechanics on large scales: for example, ice is less dense than water, which is unusual for solids to be less dense than their molten form. The reason why water is weird is because of quantum mechanics, and you can see that when you drop an ice cube into a glass of water - or, for that matter, an iceberg that a ship might crash into.

You didn't mention relativity, but it's also a place where Newtonian physics breaks down. Like quantum mechanics, relativity exists at all scales, but the effects only become significant at very high velocitie (special relativity), or over great distances or with enormous masses (general relativity).

There's a nice diagram in this wikipedia article about Classical Newtonian Mechanics vs Quantum Mechanics:

classical mechanics

The diagram shows that:

1. Classical Newtonian mechanics deals with things that are larger - generally large enough to see, and quantum mechanics deals with things that are tiny - a nanometer or less, which is the size of atoms.

2. Classical Mechanics deals with things that move somewhat slowly, while quantum mechanics deals with things that move at something like the speed of light.

Quantum mechanics starts to dominate over classical, Newtonian, mechanics, when the mass of a particle gets down to small scales, such as the range of 10^-9 meters.

We know that light acts both like a wave and a particle. This is true for massive particles, too. However, these waves are not quite like sine and cosine waves, but more like probability distributions, looking like a bell curve. A wave for a massive particle would be the probability of finding that particle in a certain region. For very very massive particles, this probability distribution becomes so small, that we say the particle is most definitely in one place, and not distributed over some region. When the mass of a particle gets to smaller ranges, we start to see probability distributions. These depend on the potential and kinetic energy of the particle. as a low energy particle will want to be in areas of lower energy.

I hope this answers your question on quantum mechanics. Visualizing this property of mass is very counterintuitive, however it is key to understanding the basics of atoms, electron structures, and optics!