Dissolving the question is the act of making a question no longer necessary: satisfying all associated curiosity, resolving all related confusions, but without answering the question. The classic example is the question "If a tree falls in a forest and no one hears it, does it make a sound?". The apparent paradox of the question is, in this case, resolved by pointing out the ambiguity of the term "sound". The question can be dissolved by distinguishing between "Sound" as referring to auditory experience and "Sound" as referring to vibrations in the air.
“Many philosophers—particularly amateur philosophers, and ancient philosophers—share a dangerous instinct: If you give them a question, they try to answer it.” - Eliezer Yudkowsky, Dissolving the Question
Sometimes a question does have a strong answer as stated, but also needs to be dissolved. This is (arguably) the case with Free Will, for example:
This is (probably) not just a case of "the other side is being silly": there does indeed seem to be something weird about the question which deserves scrutiny.
In other words, answering the question doesn't fully address the confusion that the question represents!
A failure mode in this step is giving justifications instead of explaining the process itself. Arguing that the reason we have an illusion of free will was that it was evolutionarily adaptive falls into this failure mode, as it doesn't explain the cognitive algorithm which produces the feeling of free will, and so doesn't dissolve the question. This can also be thought of as answering the "Why" instead of the "How", or as failing to provide a gears level model.
Dissolving a question usually (always?) involves providing a cognitive reduction of the question.
See also: deconfusion, cognitive reduction