The optimization process and recommendations:

1. Avoid Calling Functions With Indexed Columns (query line: 18): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index. For example, if the column `date` is indexed, the index won’t be used as it’s wrapped with the function `MONTH`. If you can’t find an alternative condition that won’t use a function call, a possible solution is to store the required value in a new indexed column.
2. Avoid Calling Functions With Indexed Columns (query line: 19): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index. For example, if the column `date` is indexed, the index won’t be used as it’s wrapped with the function `YEAR`. If you can’t find an alternative condition that won’t use a function call, a possible solution is to store the required value in a new indexed column.
3. Explicitly ORDER BY After GROUP BY (modified query below): By default, the database sorts all 'GROUP BY col1, col2, ...' queries as if you specified 'ORDER BY col1, col2, ...' in the query as well. If a query includes a GROUP BY clause but you want to avoid the overhead of sorting the result, you can suppress sorting by specifying 'ORDER BY NULL'.

The optimized query:

SELECT
        DATE_FORMAT(`date`,
        "%Y-%m-01 00:00:00") AS `date`,
        aggregate_data.offer_id,
        aggregate_data.country,
        @sum_impressions := SUM(aggregate_data.impressions),
        @sum_clicks := SUM(aggregate_data.clicks),
        @sum_leads := SUM(aggregate_data.leads),
        @sum_payout := SUM(aggregate_data.payout),
        @sum_revenue := SUM(aggregate_data.revenue) 
    FROM
        aggregate_data 
    WHERE
        `date` >= '2012-12-00 00:00:00' 
    GROUP BY
        aggregate_data.country,
        aggregate_data.offer_id,
        MONTH(`date`),
        YEAR(`date`) 
    ORDER BY
        NULL