It means more curious or more inquisitive.
Here's how it's used:
* "The child became curiouser and curiouser about the strange box." (Meaning the child was increasingly interested in the box.)
* "The scientist was curiouser than ever to discover the answer to the riddle." (Meaning the scientist's curiosity had grown stronger.)
It's important to note that "curiouser" is a more informal and playful way of saying "more curious". It's often used in literature and poetry to create a whimsical or childlike tone.