Morton Benson dictionary has "snack, bite" for this, which is completely wrong, or at least missing the main point: meze is what one eats while drinking, or to aid drinking. For snacks there are other words - prezalogajiti, labrcnuti, prihvatiti se (all verbs, true to the nature of the language).
See meze. To eat something while drinking, or something to go with drinking. It's usually bits of cheese (old or young), ham, pršut (prosciutto), and other suhomesnati (dry meats) products.