There are different ways of overhauling an engine. Most workshops do what is called an in-chassis rebuild. This is where you don't remove the engine from the car, you just pull what you need to do the job of it and do a minor overhaul - replace the cylinder liners, pistons (if they need it), piston rings, replace the big end and crankshaft bearings, lap the valves in and replace the valve stem seals, strip and check the oil pump, replace the gaskets and seals Just what is needed to be done to bring the engine back to factory specification and performance.
A major overhaul or out-of chassis rebuild is much more thorough. The engine is removed from the car (obviously) and totally stripped down - every nut and bolt are removed, cleaned, checked. Most moving parts are replaced with brand new factory stock parts - often the only original parts of an engine that has been MO'ed are the block casting, the head casting, the crankshaft, conrods, flywheel and camshaft. If any of those aren't in serviceable condition they get switched out too. And the motor gets a fresh paint job. A MO is much more expensive, but it's like you get a brand new engine back, while still usually costing less than actually buying a brand new engine.
Then there is the process of 'blueprinting' an engine. This is a MO, but much more detailed. There are manufacturing tolerances that mean there can be slight differences between two parts that essentially are the same. They are the same, only not quite. Blueprinting fixes that. All the parts that are supposed to be the same, are exactly the same. Conrods and pistons are weight matched and balanced. The crankshaft is also perfectly balanced, instead of "close enough is good enough". When you replace bearings with stock parts, once again there are manufacturing tolerances. Some crankshaft and camshaft bearing journals are ever so slightly bigger or smaller than others and with stock bearings, this causes extra friction and slight loss of power. When you blueprint an engine, you custom fit bearings to each individual journal.
To put it simply, if you had two brand new engines, one factory stock, right off the test dyno at the assembly plant and just been finished 'running in', and one that had been "blueprinted" (but still stock, no aftermarket performance parts) by a performance workshop, and compared the two, the blueprinted motor would not only start easier, run quieter and smoother, but also use slightly less fuel, and make a little more horsepower. It would also be more responsive and rev quicker.