Literally 'great air.' As a scientific term it means 'atmosphere.' As an adjective describing style, it means 'imposing and generous' - the opposite of petty or fussy.
As a compliment, 大气 means 'classy, imposing, generous in style' - the opposite of 小气 (xiǎoqì, 'petty/stingy'). You can describe architecture, fashion, a person's manner, or even handwriting as 大气.
