What is the importance of agriculture to economics?

Great importance! Starting with: if people don't eat, they can't work. Productivity falls, GDP falls, etc., etc. Additionally, if a country does not have their own food supply it is "beholden" to importing it. In times of war or economic distress this can be very damaging to an economy. In Japan, a certain amount of land is legally "reserved" for agriculture because this island nation does not want to be fully dependent on imports for its foodstuffs. A hard lesson learned during World War II.