The changes will not automatically be committed to the database when using the edit events, only the data source bound to the grid will be updated and the time of this update depends on the value of your UpdateSourceTrigger, a property on the Datagrid Control.
To save the data in the database, you would have to handle the Click event on the button, establish a connection to your database and update it based on the information contained in the bound Data source. You could do that via Sql statements and SqlConnection/SqlAdapter if you are using a SQl server. For other type of servers, you would have to use the appropriate classes.
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