Is Laser Hair Removal Painful?

The level of discomfort depends on the treated area, the texture of the hair, and skin. Darker skin people are more sensitive because they have more pigment, not just in the hair, but in their skin as well. Patients with dark and coarse hair experience more discomfort as well. After each treatment, the hair becomes lighter or thinner and the pain subsides, which makes it easier to handle the laser.
To help with the discomfort during the procedure I would recommend using a cooling device, such as Zimmer, applying a tropical anesthetic, or simply icing the area for a few minutes.

Laser hair removal feels kind of like an elastic band snapping against your skin.  Numbing cream can be applied to improve comfort.

Laser hair removal, to most people, feels like a rubberband snap against the skin. Particular areas of the body can be more sensitive, such as the underarms, bikini, and upper lip. Each person's pain tolerance can vary. Cold compresses or anesthetic creams can reduce discomfort. Some lasers have cooling devices such as cold air or a chilled tip that also helps with making the treatments more tolerable. Laser hair removal has come a long way and the treatments are usually quick enough where the pain is not much of a problem. It definitely should not be excruciating. Always let the person doing your treatment know if the pain is not tolerable.

After giving birth, laser hair removal will not impress you. However, everyone will have a different degree of tolerance.

Pain is a very personal issue and what is very tolerable for one patient is excruciating for another. Generally speaking, any female that has given birth will fly right through laser hair removal and in fact, men usually have the most difficulty. The senation is normally described as a sharp rubber band snap to the skin and will vary by area of the body treated.
With that said, there are ways to minimize the pain of laser hair removal so that it is tolerable for all. These include:

Laser colling (chill tip).
Air colling (blown air)
Ice
Numbing cream
Pain medications