The combination of “people” (人) and “big” (大) doesn't literally translate to the final meaning. Instead, 人大 (réndà) is a shortened form (简称, jiǎnchēng) of two much longer official names:
The term 人大 (réndà) carries significant weight in two distinct spheres of Chinese society: politics and academia.
The key to understanding 人大 (réndà) is context. Chinese speakers fluidly switch between its two meanings without confusion because the topic of conversation makes the meaning obvious.
The term is used in both formal (news broadcasts, official documents) and informal (daily conversation) settings.