Longevity means that one must endeavor to lengthen and increase one’s days of life. For at its inception, every day for every person is “narrow,” that is, at the start of the day, the spiritual work that a person must do that day is extremely difficult. One must fortify oneself as much as one possibly can each day to make a start from amidst the great constriction, oppression and heaviness.
Each person must increase and progress in one’s service of Hashem, and should see to it that each successive hour is “larger” and “wider” with additional holiness than the one before it. Similarly, a person must see to it that each successive day of one’s life is “larger” and “wider” with additional holiness than the one before it.
This is the essential meaning of “length of days,” as in, “Avraham was old, advanced in his days” (Genesis 24:1), meaning that [he possessed] “length of days,” and as a result, “and G-d blessed Avraham with everything” (ibid.).
Based on Rebbe Nachman, Likutei Moharan I: 60