Point of Curly's Panties

Solution 1:

It looks like in Cave Story+ on the PC and Wii, at least, finding them unlocks Curly Mode from the main menu. It's kind of unclear whether or not that mode is present in the 3DS version; I've seen comments on the internet going both ways.

In the PC version, they do have a description, which ends with:

They have no use.

Regardless of which version you're playing, they're not used during the game itself so they'll just sit there in your inventory taking up space.

Solution 2:

Obtaining them unlocks the secret achievement Panty Raider and opens up Curly's Story mode.