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The word "verandah" is a malformation of the original Sanskrit word that somewhat survives in Bengali. The word is a culmination of two words: "Vahir" (Outside) and "Andar" (Inside a room). It means something that is considered outside but situated inside a room (or covered area).
According to the Oxford English Dictionary, the word verandah originated in India where it is found in several native languages. However, it may have been an adaptation of the Portuguese or older Spanish varanda (baranda or barandilla in modern Spanish), again borrowed from Indian languages, referring to a railing, balustrade or balcony. The distinctive style of Indian architecture evolved from a hybrid of east and west. The veranda is one of the many new hybrid architectural elements.
Although the form "verandah" is correct and very common, some authorities prefer the version without an h (the Oxford English Dictionary gives the h version as a variant, and the Guardian Style Guide says "veranda not verandah").