To snuggle is to cuddle with someone. Snuggling is a little like hugging, and it often takes place in bed.
This is a cutesy word for cute behavior: nestling or nuzzling someone. People snuggle to warm each other up or to be affectionate. People dating or married often snuggle. Close friends or siblings might snuggle, and people definitely snuggle with their pets. Snuggling is only likely to happen with people who are close; if you try to snuggle a stranger, you'll probably get arrested.