The best one can do; one's utmost effort or capacity.
これは私の精一杯です。受け取ってください。
This is the best I can do. Please accept it.
彼の精一杯の努力にもかかわらず、結果は変わらなかった。
Despite his best efforts, the result didn't change.
精一杯の笑顔で場を和ませた。
She lightened the mood with her best smile.
As hard as one can; with all one's might (adverbial use).
試験では精一杯頑張った。
I did my best on the exam.
彼女は精一杯走ったが、優勝は逃した。
She ran with all her might, but missed first place.
精一杯働いて貯金した。
I worked as hard as I could and saved money.