It is covalent bonding. The electrons are shared between the phosphorus and the chlorines.
covalent bonding is when electrons are shared between two elements.
molecular polarity is a little bit complicated, but I will try to explain ;) PCl3 is an alternation on tetrahedral molecules. It means that P has one lone pair of electrons. This pair of electrons are only attracted to the P nuclei and thus a greater freedom of motion. This means that their orbital is bigger and this pushes the 3 Cl atoms closer together. The angle between each Cl now is 107 and the angle between Cls and P is greater than 107. Now, due to this shape, and also electronegativity (Cl is more electronegative than P meaning that it tends to hog the electrons they share closer to itself), PCl3 is polar. Electrons that are shared tend to flow closer towards the Cl than the P side. Therefore, on the Cl side of the molecule it's, more negative. On the P side, it's more positive.
