Question

What can a writer describe about two characters to help develop their personalities

Answer 1

How they act and their past

Answer 2

The communication, usually done through dialogue, between the characters helps to build each other's personalities, feelings, beliefs, ideologies, and particularities, which set them apart from the rest of the characters.  

A well-written dialogue can reveal subtleties, personality, and the nuances of characters without the need of description or exposition.