The Blast Furnace
The air blown into the bottom of the furnace is heated using the hot waste gases from the top. Heat energy is valuable, and it is important not to waste any.
The coke (essentially impure carbon) burns in the blast of hot air to form carbon dioxide - a strongly exothermic reaction. This reaction is the main source of heat in the furnace.
The reduction of the haematite
At the high temperature at the bottom of the furnace, carbon dioxide reacts with carbon to produce carbon monoxide.
The function of the limestone
Iron ore isn't pure iron oxide - it also contains an assortment of rocky material. This wouldn't melt at the temperature of the furnace, and would eventually clog it up. The limestone is added to convert this into slag which melts and runs to the bottom.
The heat of the furnace decomposes the limestone to give calcium oxide.
This is an endothermic reaction, absorbing heat from the furnace. It is therefore important not to add too much limestone because it would otherwise cool the furnace.
Calcium oxide is a basic oxide and reacts with acidic oxides such as silicon dioxide present in the rock. Calcium oxide reacts with silicon dioxide to give calcium silicate.
The calcium silicate melts and runs down through the furnace to form a layer on top of the molten iron. It can be tapped off from time to time as slag.
Slag is used in road making and as "slag cement" - a final ground slag which can be used in cement, often mixed with Portland cement
http://www.chemguide.co.uk/inorganic/extraction/iron.html.