The phrase "to support the head" means to provide assistance or hold up the weight of someone's head, keeping it in an upright position. Full definition
Best child care has a lot of tasks, some of them are mentioned below: Be careful with the baby's head Support the head of the baby while you are holding them. (babysafehomes.com)
Eventually we got him to the point where he would lie down with a pillow supporting his head while watching a video on my phone. (babycenter.com)
If a head restraint isn't positioned behind an occupant's head, it can not support the head in a rear impact, but good restraint geometry by itself isn't sufficient. (iihs.org)