This is the 4531st most frequent Russian word.
высоком
The word "высоком" is the prepositional case, singular, masculine or neuter form of "высокий," meaning "high" or "tall."
In this sentence, "высоком" describes a person's height and is used as an adjective in the prepositional case.
Мы говорили о высоком человеке.
We were talking about a tall person.
Here, "высоком" indicates the physical characteristic of a ceiling in a space, showing its height, and is part of an adjective modifying "потолком."
Я вижу дом с высоком потолком.
I see a house with a high ceiling.
"Высоком" in this context metaphorically refers to noble or lofty matters and is used in a figurative sense.