Literally 'bottom-air', the breath that comes from deep in your diaphragm. Singers and orators are said to have it because their voice is supported from below; metaphorically, the 'bottom' is your preparation, evidence, or backing, what gives your words weight.
usage
Common collocations: 有底气 'have confidence', 没底气 'lack confidence', 底气十足 'brimming with confidence', 底气不足 'lacking conviction'. Closely related to 信心 but more visceral: 底气 is felt in the chest, 信心 is in the mind.