Role playing is a fun way to open the door to the idea that a relationship between you and the girl already exists. If you tell a girl about a romantic date you are going to take her on, it allows her to assume that you and she are entering into a relationship and she can begin to think in those terms. She can start to fantasize about the kinds of thing you and she can do together beginning with the role she is playing as you take her on the imaginary date.
Role playing also allows her to escape the moment in a fun way. Rather than being the girl who is being picked up by a guy in a dance club, she can be the girl on a romantic picnic with the man of her dreams. This is a much more enjoyable mental image than the one about getting picked up. Girls like to think about the future, so if you plant that image into their heads, you are more likely to get there.
In addition, role playing opens up the door to several other scenarios. For instance, if the girl is in another role, she might act differently than she otherwise would. She might take on the role of a seductress, for example, which might be the furthest thing from her everyday behavior. However, if it's fun and she's willing to step out of herself for a bit, it can lead to better things more quickly.
Finally, role playing is fun. Women are attracted to guys who like to have fun. Assigning her a role and taking on a role of your own shows them that you are that guy. You are showing her that you not only enjoy acting out new scenarios but that you can pick up beautiful women in a humorous way as well.