What does "we are cooking!" mean?
In a movie, a scientist developed a flying car.
When he and his partner first drove the car in the sky, he got so excited and he said,
"We're cooking!"
I'm so curious to know what he meant by that because he didn't cook literally.

Question

Answer

It's also used occasionally in American English - 
"Now we're cooking!"  (not "We are cooking," the phrase uses the contraction) means that the project we're working on (or actions we're taking) is going successfully.
"Now, we're cooking with gas!" means that it's going really really well.

These are both old fashioned phrases.

Answer

i think its british UK
informal old-fashioned 
"to be making good progress"or "doing something well"
The battery's recharged, give it a little more gas. Now we're cooking!

Answer

It means that you are going really fast!