There's an older tradition of rule-based machine translation. In these methods, someone really does understand exactly what the program does, in a detailed way; it's designed like other programs, according to someone's explicit understanding. There's still active research in this field; I have a friend who's very deep into it.

The trouble is that statistical MT (the things that became neural net MT) started achieving better quality metrics than rule-based MT sometime around 2008 or 2010 (if I remember correctly), and the distance between them has widened since then. Rule-based systems have gotten a little better each year, while statistical systems have gotten a lot better each year, and are also now receiving correspondingly much more investment.

The statistical systems are especially good at using context to disambiguate linguistic ambiguities. When a word has multiple meanings, human beings guess which one is relevant from overall context (merging evidence upwards and downwards from multiple layers within the language understanding process!). Statistical MT systems seem to do something somewhat similar. Much as human beings don't even perceive how we knew which meaning was relevant (but we usually guessed the right one without even thinking about it), these systems usually also guess the right one using highly contextual evidence.

Linguistic example sentences like "time flies like an arrow" (my linguistics professor suggested "I can't wait for her to take me here") are formally susceptible of many different interpretations, each of which can be considered correct, but when we see or hear such sentences within a larger context, we somehow tend to know which interpretation is most relevant and so most plausible. We might never be able to replicate some of that with consciously-engineered rulesets!