At startup, BaseCamp asks for your permission to submit anonymous usage data. This helps us decide what to focus our efforts on. The prompt for this used to be in an alert, but things have been scooted into a less obtrusive "notifications button" that you can click on to bring up this prompt.
Users may have already allowed (or disallowed) this reporting in a previous run of BaseCamp. If that's the case, the simplest way to get prompted about it again would probably be to clear your /Users/YOURUSERNAME/Library/Preferences/com.garmin.BaseCamp.plist file.
The only other reasons BaseCamp would currently ping those servers is if you use BirdsEye or choose to submit an error report after crashing.
Ah thanks. I remember having agreed to that during a beta phase.
As I didn't want to trash my whole prefs, I had a look into it and just set RegistryRoot/Software/Garmin/Settings/AllowAppAnalytics to <00>. After restart I was asked again :)
Would you tell us what kind of usage data you're collecting?