Electronic band structure I want to know why the bands like valence or conduction splits up into two parts as shown in this diagram. why the energy gaps exist with in these bands? As  you can see in this diagram that their is an energy gap with in conduction as well as valence band. what  are their physical significance? 

 A: The shape of the bands depends on how the atomic orbitals interact with their neighbors in the crystal as a function of wavevector $k$ - where $k$ represents a phase shift from atom to atom.  When the orbitals of nearest neighbors overlap a small change of phase will change the nature of the overlap and, thus, of the energy level.  In many familiar semiconductors the lowest conduction and highest valence bands correspond to the anti-bonding and bonding levels of $sp^3$ hybridized orbitals in the diamond or zinc-blende structure.  In such cases the gap between bonding and anti-bonding is the band gap which makes the crystal a semiconductor.  Orbitals involved in bonding tend to have large overlap and a strong dependence of energy on $k$.
Now, the answer to your question:
However, there are other atomic orbitals as well.  For example, in silicon there are unfilled $3d$ levels which lie higher up in energy.  The $d$ orbitals do not overlap with neighbors as much as $s$ and $p$ orbitals tend to, and they result in very flat bands.  Flat bands are less likely to overlap with other bands in energy and can create additional gaps in the band structure.  
Deeper levels that are lower in energy and filled also tend to have lower principal quantum number, $n$, and are thus more deeply bound in the atoms and thus less liklely to overlap with one another and also result in flat bands lying deep in the valence structure - possibly also creating additional gaps there.
Most semiconductors physicists study just the lowest few conduction bands and the highest few valence bands because it is the filling and unfilling of these levels near the main band gap that determine the properties of fabricated devices like transistors.  Studying the more distant bands is less common.
A: The band get its name because it encompasses the range of different energy levels which an electron can take. As long as their energy is high enough, they will lie inside the conduction band. 
As for gap, that is because energy can not take continuous values (Quantized) and that is why a gap exists between electrons that lie inside the conduction band.
A: The reason is that electron orbitals are quantised. In a crystal an electron can have linear momentum, $\hbar \vec k$. This is described by crystal orbital, which are basically linear combinations of atomic orbitals at crystal site $\vec r_i$ with coefficients $e^{i\vec k \cdot \vec r_i}$. The energy of such orbitals depends on the value of $\vec k$ which is why the curves are not horizontal and straight but go up and down as a function of $\vec k$ forming bands. If the variation of energy with $\vec k$ or band width is large enough, crystal bands overlap. If not there is a gap. The other important parameter is on-site repulsion. If this is large then different bands are pushed apart. It is the ration of bandwidth to on-site repulsion that  in the simple Hubbard model determines whether a crystal behaves like a metal or like a semiconductor / insulator.
