Engine revving issue Options

[turnaround89]

When i start my car and let it idle and lightly press the gas pedal, the engine does exactly what it should, rev up really smoothly. However, my issue is when you step on the gas pedal quickly the engine almost dies. If you leave your foot on the pedal it will pull its way through this dying/stale thing it does. What would cause this stale/almost dying issue when you try to quickly accelerate, but doesn't happen when you lightly press down the pedal?

This is kind of hard to explain, but i hope i explained it well enough for someone to help me out. The problem is annoying while driving and trying to accelerate across an intersection and the car almost dying. I want to acclerate and have the car do what its supposed to do!!

Thanks everybody!!!