When you first get your new brakes installed, there’s one thing that will happen with these new brakes in the first 500 miles:
The brake lining still needs to seat in the surface of the brake rotors.
This is a normal function in a brand new set of brakes. And “seating” will occur naturally with steady driving and fairly careful braking. Meaning, not waiting until the last second to start to brake at every light or stop.
You can definitely apply your brakes fully and completely when your vehicle comes right out of the shop. Just give yourself plenty of time to brake at all stops and lights. Try not to gun or work your brakes really hard during those first 500 miles.
Otherwise, you run the risk of overheating the brake pads. What happens is, they’ll get “glazed” (from overheating). The glaze changes the texture on the pad and can create squeaking in your new brakes.
Actually, yes. For one reason and one concern (sort of related):
Reason - The pads and rotors need to become "used" to each other or have a break-in period. The pads will brake down slightly until the point where the mating surface has full contact with the rotor. It takes a little while for this to happen.
Concern - The brakes need time to "bed". This is the period where they go through heating/cooling cycles. It is a period of time where the "glue" (bonding agent) has time to fully cure. If you are not easy on the brakes during this time, the glue will move toward the surface (towards the heat). In doing so, once the thicker portion of glue is worn through, this will cause the brakes to wear out quickly. EDIT: After reviewing some information provided by @Larry, it was brought to my attention what I provided is not complete in the sense the main reason for bedding the brakes is to evenly distribute brake material throughout the rotor. Properly bedding the brakes will help prevent what most of us consider warped brake feel, which is very often mis-diagnosed. Please review these three links about bedding in procedures or follow the manufacturers recommendations as you see fit. Just know, it is a very important step. Bed-in procedural sources: Centric Parts, Tire Rack, and Zechhausen Racing (which also has a video about the importance of the bedding in process from Stop Tech). Thanks Larry for providing the links - I thought they should be here in the meat for common consumption.
In both cases, you need to allow approximately 100 miles (~160km) for both things to occur. Give yourself longer braking distances so you don't have to do emergency braking unless ABSOLUTELY needed. It's still there if you need it, but just try to be gentle. If after the hundred miles they still feel "squishy" or aren't work working up to expectation, I'd take it back to the shop to see if there are any issues.