According to US Census Data (put into table form by this Wiki article) Ohio nearly doubled its population in every decade between 1800 and 1840. What led to this explosive population growth?
I'm only familiar with the Connecticut Western Reserve (which includes Cleveland) as that's where I hail from, but maybe it'll answer your question to an extent for at least the particular region.
The Western Reserve was a large chunk of Northeast Ohio, owned by Connecticut in the 1700's. Right before the turn of the 1800's, the land was sold off, surveyed, and divided into townships for settling. Cleveland was founded in 1796 at the mouth of the Cuyahoga River, along with many of today's surrounding suburbs during that time. Ohio was granted statehood soon after in 1803. Cleveland and the area become big in industry (mainly steel), and a lot of shipping took place with the Lakes. This brought in immigrants looking for industrial jobs, and culture and education grew in the region.
The page I linked up top gives a nice overview of it all. That's just the region of Northeast Ohio - I don't know much about the rest.