why can substances exist in all three states? Please explain the triple state molecularily. Also how to read triple phase diagrams.

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Attractions between matter involve VanderWaals forces not chemical bonds.  Some materials like water have very strong VDW forces while others like CO2 have little forces.  Particles are in motion even if they are solids.  Some particles have more KE than others though the average KE is related to the temperature of the material  High KE particles may be able to break the weak VDW forces to become a vapor, right off the solid.  This is particularly so for low atmospheric pressures and higher temperatures.  Given the right pressure and temperatures solid, liquid and gas particles will exist simultaneously in the triple point.  Watch the slope of the solid liquid line on the phase diagram.  If it is negative (sloping left) like for water, then increasing the pressure will drive the material into a liquid state!  Remember water has increased volume as a solid so increasing the pressure will reduce the volume if the material becomes a liquid.  Most materials have a positive slope here.