They can be thought of the clutch of an automatic transmission.
Say a stock torque converter stalls at 1800RPM on a stock Mustang. If you were to keep your foot on the brake, and apply throttle at the same time, you could bring the RPM up to the "stall" speed, or 1800RPM before the converter begins to apply full transfer of power through the transmission, and to the drive wheels.
With an aftermarket converter, often the largest benefit is that there's a variety of stall speeds to choose from. A lot of people choose a 3k RPM stall for a bolt on, geared GT. This essentially gives an extra 1200RPM to launch at. By launching at a higher RPM, the car is making more power and will reach its point of peak power more quickly since it doesn't have to climb through the extra RPM.
A locking converter will stop the free-spinning of the converter at a certain RPM in a certain gear. Think of a direct connection between the engine and transmission, like you always have on a manual transmission car. If you press the gas when the TC is locked, the RPM's will not fluctuate outside of rising with the increase of MPH.
On a non-locking stall, it never locks, and never has that "direct" connection with the trans. If you hit the gas in a non-locking converter, or a locking converter that has yet to lock, you'll notice the RPM's raise faster than the engine is actually acceleration the car.