Something coherent is logical and clear. "I told you if you didn't do your homework you couldn't watch TV. You didn't do your homework so you can't watch TV." This is a coherent argument (and annoying as well).
The thing about such coherent arguments, as your Mom well knows, is that they are also easily and clearly understood. If someone speaks coherently, they are speaking clearly and lucidly. A slight variation on the meaning comes in the sense of something that is united clearly as a whole and a recognizable entity. You might say, for example, that New York City is a "culturally coherent region" within the United States.