The expression translates as 'to drown the fish', which is a pretty odd thing to try and do, considering fish live under water.
Noyer le poisson, however, has nothing to do with either fishing or drowning anyone - at least not literally. It is the act of willfully distracting, or confusing the other party with complications and irrelevant facts in order to achieve a set goal. The goal is usually to avoid facing a problem, answering a tricky question, or having a frank discussion about a delicate topic.
Similar English expressions would be to bamboozle, muddy the waters or create a smokescreen, all of which imply that someone makes it difficult for the other party to see what's what. Noyer le poisson adds the notion that one muddies the waters on purpose, as an avoidance strategy.
In the 1800's, fishermen used the expression noyer le poisson to describe a fishing technique aimed at exhausting a big fish hooked on the line: they would pull the fish out of the water and back in repeatedly until the fish was so confused and tired that it would stop resisting. The expression gradually found its way into everyday language as a metaphor for attempts at confusing someone until they give in, just like a fish on the hook.
Au lieu de noyer le poisson, je crois qu'il faut faire face au problème.
I believe we must face the problem, not sidestep it.
Les politiciens savent bien noyer le poisson quand ça les arrange.
Politicians know how to muddy the waters whenever convenient.