The phrase "use your head" generally means "Think it through, dummy". In jiu jitsu though, there's a very physical way to "use your head" which is underutilized even at the highest levels. Amusingly, this too is a consequence of failing to notice that we're in the system too.
We like to back up and gain perspective, separating our eyeballs from the system of bodies we're observing, to figure out what it is we want to do next. The perspective this gives is missing something very important though; it's missing your head.
Your head is an important part of the system. It's your fifth limb, in a sport that is all about doubling up on your opponent's limbs — including their head and neck, which is obviously fair game because you can see it. You'd never look at your hand and think "Yeah, that thing floating around just pointing at shit is fine". When you look at your hand it becomes obvious that it needs a job, so you do something with it. There's always things to do. Attend to the position of your own head, as part of the system you're optimizing, and you will immediately notice the importance of using it to do things as well.
When passing guard, it is a post. It keeps them from sitting up and attacking our arms and legs. "Hands off the mat!" is still a decent rule, but they can't kimura you when your head is in their chest. It's a lot harder to snag a single when your opponent's head is between you and their legs, which is why wrestlers don't stand upright and approach an opponent on a lowered level. Standing tall with your head out of play doesn't get any wiser when your opponent is so low he's seated.
As you pass and begin to climb up their body, this means keeping contact between their body and your head. No letting frames in. Maintaining a division so that they cannot connect their hands in front of you. As you climb up, your head can control the space between their head and their shoulders. They can no longer turn in because your head blocks their jaw and face from turning in that direction. They can no longer close the space between their neck and shoulder because your head is there, keeping it open. This means arm triangle setups can work, even when the guy isn't voluntarily staying on his back to avoid back exposure. This means you don't even need the arm, because no-gi ezekiels work once there's no place to turn in.
On the back, your head takes the same spot, prying their neck from their shoulder to make room for your choking arm. It holds position so that you can hang inverted off their head without hooks, and without falling off. It bends their spine such that their body must follow to where you lead them. Perhaps most strikingly, it pushes their neck into the choke, allowing you to choke from the seatbelt, with your choking wrist still in front of their throat. It allows us to break what we thought were the rules for a rear naked choke, because with their head controlled on both sides we can do what we do with guillotines.