When combined, `认识 (rènshi)` means to be acquainted with someone. Adding the negator `不 (bù)` at the beginning simply flips the meaning to “to *not* be acquainted with.”
The distinction between who you `认识 (rènshi)` and who you `不认识 (bù rènshi)` is a foundational element of Chinese social interaction. It draws a clear line between your “in-group” (family, friends, colleagues) and outsiders. The most important cultural and linguistic point for a learner is the strict distinction between `不认识 (bù rènshi)` and `不知道 (bù zhīdào)`.
In Western culture, the verb “to know” covers both meanings. Saying “I don't know him” could mean you've never met him or you don't know what he's been up to. In Chinese, these are two completely different ideas expressed with different words. Using `不认识` correctly shows a deeper understanding of this social distinction. Stating `我不认识你 (Wǒ bù rènshi nǐ)` is a neutral statement of fact, but depending on the tone, it can be a firm way of establishing a social boundary with a stranger.
`不认识` is an everyday phrase used in a variety of contexts.
The single biggest mistake English speakers make is confusing `不认识 (bù rènshi)` with `不知道 (bù zhīdào)`.