The number of moves and pushes are counted. One score is better than another, if the number of moves is less and the number of pushes is less or equal, or the number of moves is less or equal and the number of pushes is less. This means that two scores can't be compared if one has fewer moves but more pushes or vice versa. Scores are saved in a SQLite database. The file is called Sokoban.db and stored in the Scores folder.

The statistics toolbar shows four different counters with the following definitions. Internet Scoring
The "Best Score" toolbar shows best scores from a global internet database. When opening a level, the best score will be automatically downloaded. This score is compared to your best and if you have a better score, it will be uploaded to the global database.

The Scoreboard shows the saved scores and solutions for the currently displayed level. Each row shows the rank, player, moves and pushes, the presence of a solution, the date and the state. The scores can be sorted on best pushes or best moves on the scoreboard. Scores and or solutions can be deleted from the list. A saved solution can be loaded to the game and replayed. Select a solution on the Scoreboard by clicking a row in the list and click "Load Solution". Then use the NavBar in the main window to play the solution. The three states are:
Score Backup
It's important to regularly backup the scores database. The database file is in the Scores sub-folder. Click "Tools" - Database Handling". The dialog shows your database files. The Sokoban.db file is the one in use. The others are automatically saved copies. Click "Options" to set when copies are created. If the Sokoban.db file is broken or lost, you can restore the database with one of the copies.

You should also save a backup in a safe place. That way you can resore the database in case of hard disk failure. Use a dvd or usb-stick to regularly copy all files in the Scores folder.