You will get all the dress information with your final docs. Last year on Explorer there were 2 formal nites and 1 semi-formal, the rest casual. Formal is just that, wear your nicest clothes, cocktail dresses for woman, dark suite or tux's for the guys. Semi is still dressy, men wear sports coats, with tie. The casual the guys can wear docker type pants with polo shirts, woman wear pants outfits or dresses. No shorts or jeans are allowed in the dinning rooms for dinner, so hope this helps. Also, sometimes the dinning rooms can be chilly, so be sure to pack a sweater, you just never know.
Here is a link to a good article about "packing easy", should help:
Enjoy Expolorer, great ship, tons of fun!