Stumble Upon has started rolling out a pop-up along the control bar at the top of the page that recommends sites and interests based on the things that you Stumble frequently. If you Stumble pages on a site frequently, StumbleUpon will ask you if you would like to see more pages from that site. Likewise, if you thumbs up a lot of a certain type of interest, StumbleUpon will ask you if you would like to stumble that interest more frequently.
Search Engine Journal brought to our attention that if you like pages from them, or other sites, you will be prompted to view other things from their site. Selecting yes or no will either show you more or less from that domain as you continue to Stumble.
The in-browser app may also recommend other interests based on the interests you like the most. Search Engine Journal uses the example of fashion. When you like pages from fashion often, StumbleUpon asks you if you would like to start stumbling related interests like shopping and photography.
It is unclear if requesting a certain site actually subscribes you to their StumbleUpon account, but it does make that page appear more frequently if you choose so. For bloggers and marketers this could mean increased engagement for people that don't follow them, and possibility of increased traffic if the user likes what they see.