Explain why quantum behavior is not observed in daily life People always ask:
How come we don't see any "Wave" attached to a classical object such as a car?
You always see the object in the same place without any uncertainty. 
I am sure there are answers, but please use the simplest language understandable by general public.
 A: Quantum mechanics became necessary as an underlying framework of classical mechanics due to experimental observations that classical mechanics and classical electrodynamics could not explain.
1) The photoelectric effect, that light hitting metal extracts electrons with discrete energy characteristic if the metal,  the effect can be explained only as  a particle hitting the electron; classical electrodynamics says light is a wave with alternating electric and magnetic fields of continuous energy.
2)the periodic table of elements  which showed a limit to the fragmentation of matter into multiples of the weight of hydrogen. Classically fragmentation could be continuous and no structure could be predicted
3)black body radiation, which could not be explained with classical thermodynamics and electromagnetism. The model that fitted the data had to posit that there were particles, called photons, in the electromagnetic radiation of energy E=h*nu .
h is the Planck's constant and is the basic reason that quantum mechanical effects are not evident macroscopically. For classical mechanics h=0.  In the quantum level it is a very small number  but its value controls the dimensions in which quantum mechanical effects dominate by the Heisenberg Uncertainty Principle. This says:


(ħ is the reduced Planck constant).

As a rule of thumb, quantum mechanical effects dominate when the uncertainty in position with the uncertainty in momentum is of the order or smaller than the inequality  seen above.
Macroscopic objects in general fulfill this automatically because ħ is such a small number, $6.62606957(29)×10^{-34}$ joule*seconds, that our accuracies of measuring the position and momentum of the car of the example are much larger than the variation in position and momentum  of the car due to the underlying quantum mechanical variations.  Our four senses are worse than our measuring instruments, of course.
So classical physics is adequate to describe experiments and situations where h is effectively zero.
The quantum mechanical effects surviving macroscopically are second level effects, like transistors, or the regularity of crystals, or the above numbered three discrepancies with classical physics. As other answers state one can prove mathematically that quantum mechanical solutions at the limit end up in classical solutions, though it needs quite some mathematical background to understand it is so.
A: This because though quantum physics applies everywhere, classical mechanics is a good approximation. Just like in special relativity, where as v -> 0 (or we as assume c -> $\infty$), Newton's equations become more valid, the same thing happens in quantum mechanics.
In quantum mechanics, this called the Correspondence Principle. It formally says that as n (quantum number) -> $\infty$, Newton's classical mechanics becomes more correct, but a simpler (though somewhat less correct) way of putting it is that as we "zoom out" (i.e. go to larger scales) classical mechanics provides an accurate approximation.
Also, in your car example, it hs to do with wavelength. The highest the momentum of a particle, the shorter its wavelength. A car has tremendous momentum compared with an electron or photon. As a consequence, its wavelength is small. As wavelengths get smaller, wave-like properties diminish and particle-like properties emerge.
That being said, we can observe quantum phenomena: lasers, the photoelectric effect, heat radiation, etc. 
A: I will start with the short version of the answer and then move to a little longer version of it.

We do not observe quantum behavior in real life because of the
  limitations of our biological architecture.

A little longer version
We didn't need to have evolutionary traits that are attuned to quantum phenomena. It is the reason why quantum physics seems so queer. An untrained person doesn't have a vocabulary to express the phenomena of an object being in two opposite states at the same time. 
For example, a quantum coin could be in a state of both head and tail. How is that possible? How can it be? Well, our tongues can't articulate it. In fact, this whole thing about light being both wave and particle is a hype. This is used like a catchphrase, but all it shows that we don't have a large enough vocabulary to describe the nature of light and other quantum objects. And that's okay! In real life, we catch a ball and not an electron.
That's why, in real life, quantum phenomena is not observed.

Just because it's not observed, doesn't mean it doesn't occur
@Jon Custer, mentioned about laser in the comments, and I'll mention that here too. Every time you are in a presentation, and the presenter uses the laser pointer, quantum phenomena is occurring. Sun shines, and the explanation of the mechanism needs quantum physics. We have food because of photosynthesis, and that's a quantum phenomenon too. You observe quantum phenomena all the time, if you define observing by both sensing the event and acknowledging the mechanism behind it.
The last thing I'll comment on in this answer, is the "associated wave with a particle" thing that you mentioned in the question. There's this fundamental constant in quantum physics, called the Planck's constant, $\hbar$. I could write down its value and then tell you how disastrously small it is. I won't do that because, $\hbar$ is a constant with physical units. You can say 2 is a small number. But, you cannot say 2 m is small, because it's a large distance for an ant, and small distance for an athlete.
As far as the $\hbar$ is concerned, we're giants compared to it. By 'we', I mean our coarse senses. Again, $\hbar$ isn't small, our senses are accustomed to too large of things!
A: According to this article, we can’t observe quantum effects of large-scale objects (such as a car) because we live in a strong gravitational field caused by the Earth. General Relativity says that a gravitational field causes time dilation.

… when an object is in superposition, all its parts vibrate in synchrony. However, time dilation will cause parts of that object that are at slightly higher altitudes to jitter at different frequencies than parts at slightly lower altitudes … The greater the difference in altitude between parts, the greater the mismatch. For a big enough object, the mismatch grows big enough to disrupt superpositions.

When superpositions are disrupted, the wave functions collapse. That’s why we know with absolute certainty the position and velocity of classical objects.
And, if we want to observe quantum effects more clearly, we should conduct more experiments in space and at very cold temperatures.

UPDATE: I found the original article: Universal decoherence due to gravitational time dilation
further readings:


*

*Physicists Eye Quantum-Gravity Interface

*Researchers explain why quantum behaviour doesn’t occur in everyday life

*Are there examples of quantum mechanics that can be seen in every-day life, or do they only show up in the lab?

A: Actually, Heisenberg's uncertainty principle certainly appears in everyday life, and in some cases, drives what we see classically.
Take for example a pencil balanced on its point. Assume you want to know the length of time that it can be balanced on its point.
So, the standard thing to do is to consider a pencil with mass $m$ and length $l$, something like an inverted pendulum. Using the small-angle approximation, you get the second-order pendulum equation ODE, which has solutions:
$\theta(t) = A \exp \left[\sqrt{g/L}t\right] + B \exp \left[-\sqrt{g/L}t\right]$. 
Now, we can obtain canonical variables (as are used in Heisenberg's uncertainty principle) by computing:
$x_{0} = \theta(0) L = (A+B)L$, and $p_{0} = m \dot{\theta} L = m \sqrt{gL}(A-B)$.
Now, the product is:
$x_{0} p_{0} = m \sqrt{g} L^{3/2} (A^2-B^2) \equiv \hbar$.  Ignore $B$ since it's just a constant, and the pencil will fall when it is tilted by $1^{\circ}$, so solving for the time, we get:
$T = \sqrt{L/g} \left[(1/4) \log \frac{m^2 g L^3}{\hbar^2} - \log(180/\pi)\right]$.
The first term is much larger! So, Quantum Mechanics is driving this very classical apparatus. This is very suprising and yet strange, that Heisenberg's uncertainty principle can also be applied to classical mechanics.
