It means he/she was not a person who accepted the second choice. He/she always wanted the best of everything.
Here are some literary examples of " second best".
" And when Anne, dressed in her second best, as primly opened it, both little girls shook hands as gravely as if they had never met before."
Anne Of Green Gables by Lucy Montgomery.
" She was wearing a black cashmere dress that had been her aunt Jane's second best."
Rebecca Of Sunnybrook Farm by Kate Wiggin