Trigger for updating a count of rows from a table into another table
Yes, you could do this via a Trigger. But you would need 3 triggers: 1 on insert, 1 on delete, 1 on update (which would do nothing, unless you modify the Item column). This would be harder to mantain, and would slow down operations in orders table.

Another option is using a view:

CREATE OR REPLACE VIEW `ordered_items`
    AS
        SELECT `Item`, COUNT(*) AS `Qty`
            FROM `orders`
            GROUP BY `Item`;


The drawback is that reading ordered_items is slower, because the GROUP BY on orders is executed each time. If this is a problem, you could periodically copy data from ordered_items view into a physical table. This could be done nightly via an Event, if you have MANY data.