The Clients tab will show you all the bookings on which you have been requested and a list of all the customers who have added you to their Pro Team.
Under Job Requests you will find your Exclusive Request and Other Requests.
Exclusive Requests are bookings where you are have either been listed as the customer's Favorite professional, or the customer has created their booking using your profile page. If you're interested in any of these bookings make sure you claim them as soon as you are able, they won't stay exclusive forever.
Other Requests are bookings from customers who have you on their Pro Teams. These are people who either worked with you before, or liked what they saw when they reviewed your Handy stats (ratings, and job count).
You can see a full list of the customers who have you on their pro team by clicking Clients, at the top of this tab. This view will show you a few details about your clients, namely neighborhood, the last time you worked together, the date of their upcoming booking, total earnings with their bookings, and their photo (if they have provided one).