. . . . . . . . Andamans are situated in the Bay of Bengal while . . . . . . . . Sicily is a beautiful island.

Before most proper nouns, like names of people, continents, countries, cities, etc, the use of an article is omitted. As 'Sicily' is the name of a city, (which is an island), no article precedes this word.
However, before certain proper names, especially names of places, the definite article 'the' is used. The word 'Andamans' is one such proper name which denotes the name of a place (a group of islands). Other examples are: 'the Himalayas', the Sahara', 'the West Indies', etc.