1: To submit a story on the popular social networking website, digg
.com. The website is a way for users to share web content and news articles on the internet. In past tense, you say you "dugg it."
2: To really like something. The spelling is usually only with one g in this instance (dig, not digg).
1: This is a great article. I'm going to digg it right now.
2: Dude, I totally dig it!