How can we write the wave function in quantum mechanics? In quantum mechanics, while writing the wave functions we can take a product of the spatial and the spin parts.But what does it means? What is the meaning of the spatial wave function and the spin wave function?
The wavefunction contains all the information about the system of interest.  This is a basic premise of quantum mechanics.  

Within the Born-Oppenheimer approximation, we 'index' all the values required to describe where an electron is.  This includes the spatial coordinates, ($\textbf{r}$), and the spin coordinate, $\omega$.  Electrons are characterized by their spin ($\uparrow$ vs. $\downarrow$).  Another way to think about it is this.  The quantum numbers are used to describe everything we need to know about 'where' an electron is ($n$, $l$, $m_l$, $m_s$).  The spatial coordinates (e.g. Cartesian coordinates) take care of the first 3 quantum numbers.  We need the fourth coordinate to characterize $m_s$.