This is the 12966th most frequent Russian word.
личная
"Personal."
Here, 'личная' describes the nature of the problem, emphasizing its private and individuality-related characteristics.
У меня есть личная проблема, с которой я сейчас сталкиваюсь.
I have a personal problem that I am currently facing.
In this context, 'личная' pertains to 'life,' signifying an area that is private and specific to the individual.
Её личная жизнь всегда была закрыта от общения.
Her personal life has always been closed to communication.
The word 'личная' here modifies 'вещь,' indicating that the matter is of a private or intimate nature specific to the speaker.