This is the 5007th most frequent Russian word.
личную
"Personal" (accusative singular feminine form).
In this sentence, 'личную' is used as an adjective describing 'точку зрения' (point of view), signifying that it is personal or individual to someone.
Я ценю твою личную точку зрения.
I value your personal point of view.
Here, 'личную' describes 'ответственность' (responsibility), indicating that the responsibility is individually assumed by him.
Он всегда берет на себя личную ответственность.
He always takes personal responsibility.
In this sentence, 'личную' (referring to 'личное пространство' in full) is used metaphorically to denote someone's private space, emphasizing individuality and privacy.