Here's why:
* Phosphorus (P) has 5 valence electrons.
* Chlorine (Cl) has 7 valence electrons.
* In PCl3, phosphorus forms 3 single bonds with 3 chlorine atoms. This uses up 3 of phosphorus's valence electrons.
* The remaining 2 valence electrons on phosphorus form a lone pair.
You can visualize this with a Lewis structure, where the lone pair is shown as two dots on the phosphorus atom.