When someone snugs, they move closer to someone else to show love or to get warm.
Snugging is usually a nice thing because it means someone wants to be close to you.
Examples:
The puppy snugs up to its owner for warmth.
She snugs her teddy bear when she goes to sleep.
He snugs with his family on the couch.
The cat snugs up to the fire to get warm.
The baby snugs with its blanket at bedtime.
The friends snugs together to take a picture.