From testing it out, each snap that's sent or received represents one point. Posting a snap to stories also increases your score by a point while texts sent or received and viewing stories aren't counted.

Does viewing snap stories increase score?

You receive a point for sending a Snap, you receive a point for opening a Snap, but there are no points for just messaging on Snapchat. ... Unfortunately, Snapchat scores do not increase if you watch a story.

Do you get points for looking at Snapchat stories?

Post Snapchat Stories daily

A Snapchat story gives you one point per snap that you post. You do not get points based on how many users view your Stories.