The default privacy for your activities is offline. That means that as standard all activities are saved to the app's local History section in the app. To back up your activities it is recommended that each one is synced to your online profile on www.mapmytracks.com.
Sync with website from the History section in the app.
To sync any activity to your Map My Tracks account first open the app's menu and tap on History.
Then for the activity you want to sync tap on the options icon (3 dots) and choose 'Sync with website'.
Sync with website after finishing an activity.
To sync the activity that has just been completed tap on the options icon (3 dots) and choose 'Sync with website'