This article explains the concept of a creating Contact on the Fly (Quick-add). For example: If you are creating a Project and for billing purpose you want to add a new contact, you can add by a Quick-add option present in the dropdown box of the Contact field.

While creating a project you feel to add a new contact.

1. Go to the contact field. (In this case Billing Contact in above image)
2. Click on the "V" button for drop down list.
3. Click on the "+" button in the bottom left corner of the list.

It will open a pop-up window to create a contact.