I assume you are talking about Act 1, scene v, when Romeo attends the Capulets party.  Remember that Romeo is esentially in a no man's land, as he is in the house of his sworn enemy, an enemy with whom he had an altercation earlier in the day before the party.  It was absolutely necessary for him to wear a disguise for the event, and for the period, hand-held masks, for both men and women were not uncommon.  This allowed him the freedom to reveal himself to Juliet at their meeting, but to keep it hidden when necessary, as with Tybalt, although he discovered his identity anyway in the long run. It is also important to the drama in other ways, as well.  It serves to heighten the animosity Tybalt feels for Romeo and all the Montagues because he has had the nerve to appear in the Capulet house, even in disguise, and Tybalt feels as if the Capulets are being mocked by the Montagues.

Romeo must go to the Capulets' party in disguise because he is a Montague, and the two families are feuding, perhaps even warring. If he weren't in disguise, he wouldn't get in. Therefore, it is somewhat important to the scene's tension. It's also important because it allows both he and Juliet to fall for one another without knowing who the other is.

As for what he could wear, it should be something relatively simple, so he can drop it when stunned by Juliet's beauty (and, practically, so Tybalt can pierce it easily).