You are pretty on point with your own idea: " ...often summed up with intelligence or cleverness?". By my knowing; " She would have the brains for this murder " in your example, is an expression. " Having the brains to do something " is a way of saying: I, he, she or it is smart enough to come up with a certain something and execute it. It is a way of suggesting a living thing has the intelligence to do, or think of, certain actions, ideas, etc. Like the example up next, Example: Question "Do you think she can do the task given?" Answer " She certainly has the brains for it!" ( "She" can be replaced for he, it, they, etc.) I used " suggesting" here, because it is, in essence, a guess whether or not the person, animal/insect or plant even, really does have the intelligence to come up with certain ideas or execute certain actions. -Any real teacher can come in and correct me on this, I am not a teacher here.