"Panned out" means the same thing as "turned out," "came out," and "ended up."
I think the literal reference is to panning for gold. In 1800s gold mining, miners dug up dirt that they hoped contained tiny "grains" or "flecks" of gold. They put the dirt in a pan with water. They "sluiced" the water around, stirring up the dirt. The gold flecks, being heavier, would stay at the bottom. The water would pick up the rest of the dirt. The miner could flip the water, earth, sand etc. out of the pan, leaving "gold dust" at the bottom. The gold at the bottom had been "panned out."
"It didn't pan out the way I hoped" means "I thought there would be gold in it. After I panned it out, I saw there wasn't any. I didn't pan out the way I hoped."