Is there any significance of atomic orbitals? We have been taught that the atomic orbitals we read about are probability density region of finding electrons of particular energies which are designated by the various quantum numbers.
Since, there is high degree of uncertainty when we talk about the position of merely the detection of an electron as well as the energy that we "observe" and which may pretty much not be the actual energy of the observed electron, what then is the significance of any atomic orbital?
I am not very well read in the various techniques and theories that we have developed over time, but still I think that atomic orbitals are at best a high probability region of finding certain electrons. Since we must not be able to do that with enough certainty how then can we check the validity of the existence of orbitals?
Is it possible, that the idea of atomic orbital is now outdated in terms of modern development and only used for simplistic explanations of complex electron motions and phenomenons?
Overall, I am interested in learning the significance of atomic orbitals. Google provides various links explaining the theory and listing its uses in modern chemistry but I could not find anything which properly explains the significance or even tries to explain the actual presence of something like an atomic orbital other than saying that we find so and so probability regions while working with Schrödinger equations.
Added after answers and comments: The answers are listing the uses of the contruct only, I tried to say that I am interested in finding out whether something like an orbital is actually there or not. 
Maybe an example will help, there is no boundation for an electron of certain energy to move in an orbital that is dumbled or double dumbled shaped! I agree with electrons having certain energies described by quantum numbers, but how can one definitively prove that an electron belonging to say 2p_x resides in a dumbled shaped orbital?
Again, are orbitals true? Are they actually significant and not just a helpful mathematical construct? Can it be definitively proven?
 A: Yes, atomic orbitals are very significant.  
An electron being in a particular orbital corresponds to a specific energy. If an electron transitions between two orbitals, the energy of the photon absorbed or emitted is the difference between the energy levels of the orbitals.  
The probablilty density function is also important.  For example, an s-orbital electron has a probabilty of being within the nucleus.  The gives rise to Fermi Contact Interaction, which has observable effects in NMR and ESR spectroscopy and electron capture.  
A: There is another "usefulness" of orbitals other than probabilities that I think is important to keep in mind, and is not clear from your question whether you've been introduced to it.
The wave function $\Psi(x,t)$ representing some given atomic orbital satisfies the Schrodinger equation for the atom. This means that the eigenvalue one extracts from $\Psi(x,t)$ represent that orbital's energy level. In some sense, the energy level is "encoded" in the shape of $\Psi(x,t)$ (for a given potential).
Historically, this was how Schrodinger first made use of his equation; not from a probabilistic point of view, but from deriving the hydrogen energy spectrum.
A: It's hard to pinpoint the exact cause of your confusion.
For instance, you state that "atomic orbitals are at best a high probability region of finding certain electrons. Since we must not be able to do that with enough certainty how then can we check the validity of the existence of orbitals?"
The probability in this case is a probability for a single measurement, which is entirely uncorrelated with the same type of measurement on another atom a micrometer away. If you aggregate enough measurements, the uncertainties cancel out. 
The importance of these orbitals is critical to chemists. Basic organic chemistry depends on s- and p-orbitals overlapping to form bonds. In essence, an orbital specifies where an electron pair can be (one spin up, one spin down). Where two atoms approach, they may develop a common orbital. If both atoms have orbitals with only a single unpaired electron, the common/merged orbital can hold a pair. Having an electron pair with opposite spins is energetically beneficial, which explains how the formation of such a pair in a common orbital forms a stable bond between atoms.
Even fancier orbitals exist, in particular in benzene and similar cyclic molecules. We know that benzene is pretty flat, which is the result of orbitals on either side of the ring. These give rise to the rather unusual behavior of benzene.
A: The existence of atomic orbitals as described by quantum mechanics has been directly probed in an experiment. Also, related is that STM is able to show electron density of a surface, and this density is roughly the same as electron orbital for many-atomic system.
