When MgO (magnesium oxide) reacts with NaOH (sodium hydroxide), they undergo a chemical reaction known as the metathesis reaction, or a double-displacement reaction. In this process, the ions present in the compounds exchange to form new products. The products formed in this reaction are:

1. Magnesium Hydroxide [Mg(OH)2]: This compound is formed as a result of the exchange between Mg2+ ions from MgO and OH- ions from NaOH. Magnesium hydroxide is a white, insoluble solid that finds applications as an antacid and a laxative.

2. Sodium Oxide [Na2O]: This compound is formed by the exchange between Na+ ions from NaOH and O2- ions from MgO. Sodium oxide is a white, hygroscopic solid that readily absorbs moisture and carbon dioxide from the air, forming sodium hydroxide and sodium carbonate.

The overall chemical equation for this reaction can be represented as:

MgO (s) + 2NaOH (aq) → Mg(OH)2 (s) + Na2O (s)

It's important to note that the products formed in this reaction are determined by the specific ions present in the reactants and their chemical affinities.