The two-language problem refers to the fact that many scientific codes are prototyped in a slow but flexible language (to test an idea quickly) but then have to be moved to a faster but less flexible language for practical applications. Translating from one language to another both slows things down and introduces bugs.
Julia addresses the 2-language problem by allowing for flexible prototyping which can be replaced by fast optimized code - all within Julia. This doesn’t mean that all code written in Julia is fast, but it does mean that slow code in Julia can be identified and optimized. This can now be done incrementally, which is less time-consuming and less prone to introducing bugs.