one's best; the best one can do
Used as a noun to refer to the utmost effort or limit of one's ability. Often appears in phrases like 精一杯だ (it's the best I can do) or 精一杯の (one's best possible).
This is the best I can do right now.
He answered with his best possible smile.
with all one's might; as hard as possible
Adverbial use meaning to do something to the fullest extent of one's ability. Commonly modifies verbs like 頑張る, 努力する, 走る, etc.
I'll do my very best in tomorrow's match.
He ran as hard as he could, but didn't make it in time.
Getting by on my current salary is about the most I can manage.
I greeted them with the best smile I could manage.
I have no regrets because I did my absolute best.
I want to live each day to the fullest.