This is the 13552nd most frequent Polish word.
pilnującego
"Pilnującego" means "watching," "guarding," or "overseeing" in English.
Here, 'pilnującego' is the present participle form of the verb 'pilnować', meaning 'to guard', and is used as an adjective to describe the dog.
Widzę psa pilnującego owiec.
I see a dog guarding the sheep.
In this sentence, 'pilnującego' describes the orderly state (a noun), serving as part of the participial phrase modifying 'strażnik' (the guard).
Strażnik pilnującego porządku czuwa całą noc.
The guard watching over the order stays awake all night.
Here, 'pilnującego' is describing the teacher in the context of their activity (looking after the children).