What is the difference between reversed phase and normal phase in hplc analysis?

Normal PhaseIn a very non-polar environment, hydrophilic molecules will tend to associate with each other (like water drops on an oily surface). The hydrophilic molecules in the mobile phase will tend to adsorb to the surface on the inside and outside of a particle if that surface is also hydrophilic. Increasing the polarity of the mobile phase will subsequently decrease the adsorption and ultimately cause the sample molecules to exit the column. This mechanism is called Normal Phase Chromatography. It is a very powerful technique that often requires non-polar solvents. Due to safety and environmental concerns this mode is used mostly as an analytical technique and not for process applications.

Reversed Phase

The opposite of normal phase, or Reversed Phase Chromatography, results from the adsorption of hydrophobic molecules onto a hydrophobic solid support in a polar mobile phase. Decreasing the mobile phase polarity by adding more organic solvent reduces the hydrophobic interaction between the solute and the solid support resulting in de-sorption. The more hydrophobic the molecule the more time it will spend on the solid support and the higher the concentration of organic solvent that is required to promote de-sorption. 

I think the difference is in relative polarity of mobile and stationary phases. While in normal phase LC the mobile phase is nonpolar  (must be 100% without water wich is the main limitation of normal phase LC) and stationary phase is polar (silica etc.) in reverse phase the mobile phase is polar (water) while stationary phase is more hydrophobic.

Normal phase is when the stationary phase wich is the sorbent is polar while the mobile phase is non-polar meaning the more hydrophilic the analyte is the more it will interact with the stationary phase hence increasing its retention time inside the column.

Reversed phase the staionary phase is non-polar while the mobile phase is polar meaning, if the analyte is hydrophilic ( water loving) it will interact less with the stationary phase hence less rention time inside the column.

in a normal phase chromatography, we have a polar column, while in the reversed phase chromatography, the column is hydrophobic, like a c18 column. 

Normal phase = Stationary phase is Polar. Reverse phase = Stationary phase is Apolar.