When multiple users try to edit the same record at the same time, the operation in which a user saved the record first takes precedence.
If other users try to save the record, following error message is displayed and they cannot save the record.

If this error is displayed, copy the record which you are editing and then refresh the record, or reopen the record to edit it again.
If you click Cancel or move to other screen, your edit will be deleted.

Note that, when editing a record, you cannot lock that record to prevent other users from opening the edit screen for the same record.