The island (in fact several islands located close together and connected by bridges) is best known as a place where Venetian glass is made. The history of the glassmakers on Murano Island dates back to the end of the 13th century when all glassmakers from Venice were ordered to move to Murano. Since at that time most of the city structures were wooden, the presence of the glassmakers (who use open fire for their work) was undesirable.
Soon enough, the glass made there was well known throughout Europe and the products (e.g. beads, mirrors or chandeliers) became sought-after goods. Even today, the Venetian glass is a prestigious product.
You can get to Murano by public transport (boats) that go there every 30 minutes. The local glassmakers are usually very willing to show their craft to the onlookers.