Their goal is to introduce into the target's head, the idea of dissolving his father's company. They have to be subtle, or else he'll know that the idea came from someone else, so they separate these 3 ideas into 3 separate dreams:

>First dream: "I don't want to follow in my father's footsteps."

>Second dream: "I want to create something for myself."

>Third dream: "My father doesn't want me to be him.

Each time they go deeper into a dream, the amount of time they'd be stuck in the dream if they fail is increased. Which is why they need to manually get themselves out of the dream, and why they need the music as a queue to help time everything correctly.

What they're timing is "kicks". They need to fall at the right time so they can wake up. If they fall in the first layer while they're all the way in the third layer, they'll be in too deep a sleep to wake up, and they'll just die and end up in limbo. So they have a series of kicks to wake them from the third dream layer, then the second, then the first, in succession.

I can explain more if that doesn't make sense. It's been a long while since I've seen the movie.