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
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'