Occasionally people want to check in somewhere without all their friends knowing where they are. For this reason, Foursquare provides an option to “share” the checkin with your friends. If you choose not to share with your friends, your location will show as “[off the grid]” to everyone else on your friends list.
If you want your friends to know your location, you must allow the app to share the checkin with your friends. Don’t worry about annoying your other friends with the app by telling them about your checkins. They won’t receive any special notification about your checkin unless they’ve specifically requested to receive pings from you. Your checkin will appear alongside everyone else in their friend list.
Sharing your checkins with Twitter and Facebook are also options that are completely unrelated to the “Share with friends?” checkbox.