For our purposes, there are two types of agriculture: Subsistence (food) agriculture and cash crop agriculture. The farming in the North focused on foodstuffs (corn, wheat, vegetables, etc.). The farming in the South focused on higher value cash crops, cotton, indigo, sugar, etc.
Under a subsistence economy focused on food, you don't want slaves, because they represent more mouths to feed. You want to use your farmland to grow food for your own family, not for a bunch of other people. This was true in the North, where the climate permitted people to grow only enough food for themselves (and a little extra for trade), but not for "export." Later, machines such as tractors enabled 1 person to grow food for 30-40, but those are cheaper than slaves. Enough said.
It was different in the South. Cash crops such as cotton or sugar are more valuable than food, but such crops grow best in warmer, southern latitudes. So you could employ slaves to grow these crops, sell them abroad, use the money to buy food for them and for yourself, and still make a profit. Many cash crops do not lend themselves well to mechanization, which is why slavery can be profitable.
Essentially, "agriculture" was more profitable in the South than in the North, and that's why northerners were more eager to "industrialize," while the South preferred to remain "agricultural" for longer.