What is going on inside the LS6 powertrain control module (PCM) is the front oxygen (O2) sensors are providing feedback to the PCM on how rich or lean the fuel mixture is at various intake manifold pressures and rpms. This O2 sensor feedback is stored as short-term fuel trims (STFT) and long-term fuel trims (LTFT) and tells the PCM how much fuel it needs to add or subtract to achieve stoichiometric air-fuel (A:F) ratio.
The LTFTs are generally positive values in a V which means the PCM is adding X% of fuel to meet the desired A:F. Depending on the weather, gasoline, altitude, temperature, modifications, etc., the PCM will self-learn to a limit of 13% before tripping a diagnostic trouble code (DTC) for either too lean or too rich. The LTFTs are just that - long term and are slowly updated over time and is something one would have a hard time noticing.
Driving in steady state, any V with nearly any traditional bolt-on modification will be running at the perfect 14.7:1 stoichiometric A:F. The O2 sensor feedback and resulting LTFTs will make sure of that.
So if the STFTs and LTFTs make sure the A:F is right under steady state, why would anyone need a tune? The answer: since positive fuel trims are the norm, under wide-open-throttle (WOT) the PCM says "Ah, my stored factory maps are lean and under normal driving I've had to add fuel (from the + LTFTs) so I need to add fuel as well under WOT." Since the factory WOT fueling map is on the rich side for thermal management, extra fuel during WOT isn't helping the production of power to the ground. With a properly done tune, the LTFTs will be slightly negative so the PCM does not add extra fuel to the WOT mode; thus increasing power.
A "real" part-throttle tune (can't be done on a DynoJet with a few WOT pulls) will also take into account increased air flow as well as new air (a fluid just like water) path harmonics introduced by modifications such as cold air intakes, headers and exhaust. This fine tuning across the entire engine rpm and intake manifold pressure range increases the throttle response and as a side benefit, creates more perfect fueling maps which results in smaller and more accurate LTFTs which in turn leads to more accurate WOT fueling and power production.