Why is it when I give my 06 mustang gt gas, it revs for a little then it finally kicks in?

Could be a few things. Others are sure to chime in here too but here is my first hunch:

I would check a vacuum line- I had one that went bad and it behaved similarly. If it is an automatic I might have the transmission serviced to be sure it is operating properly.

Because mustangs suck…

-Manual or Automatic?
-Turbo/NA/Super?

If its revving its getting gas, maybe something is wrong with the air flow that is keeping it from kicking properly? Is it EVERY time you give it gas, or right after putting it in drive or into gear or what? More information needed.

It sounds transmission related if the engine is actually revving and you’re just not moving.

If it’s a manual transmission, you’d hope it’s the clutch slipping. It could be due to something causing it to slip (not engaging fully, oil, coolant, or another lubricant getting in there, etc) or could just be worn out if it’s been abused.

If it’s an automatic, there’s a couple of different parts that try to transfer power to the wheels smoothly and it may be a problem there.

Either way, a mechanic is probably needed unless you really enjoy working on it.

That’s what my Duster used to do when the transmission fluid was low. Or it was about to give out.

If it’s automatic, have your rings tightened.
If it’s a stick shift, have your clutch throwout bearing checked.