Take two situtations
MC<MR.
What this means is that the revenue gained from producing one more unit exceeds the cost required to make this additional unit. Therefore a firm would increase it's production as the increase in revenue per unit is greater than the increase in cost per unit. The firm may end up having a larger cost from producing one more unit of output, but the revenue gained would be greater than the cost incurred hence the firm is more willing to produce more.
MC>MR
If MC is greater than MR then the cost of producing one more additional output exceeds the revenue gained from producing one more additional output. As a result the firm will reduce it's production levels to increase total revenue. While the firm loses some revenue due to the reduction in production, however it would not incur the associated cost at the same time. Hence the firm is more willing to cut back on its production as the reduction in revenue is less than the reduction in price.