Each time a segment is scheduled to run, two things occur:
Query is run on the database or data warehouse
For each destination, a sync request is made
In the Query History tab of each segment, you can view the query history each time a segment is scheduled to run.
Each of these records contain the number of results, as well as which destinations it was synced to (and the success of the syncs).
To get more granularity on each run, click on the destination under Active Destinations. You can see each individual sync request, whether the last attempt was successful, and any potential errors.
If there is an error, there will be a view error button in each row that will show any potential errors for debugging purposes.