The term "interpreter" on the most basic level simply means a translator, or more specifically someone who does oral translation in person as opposed to a literary translator who works primarily with written materials.
The role of the interpreter is necessitates by the linguistic situation of the Indian subcontinent. India has over 122 major languages, and many different dialects. Over 29 Indian languages have more than one million native speakers. There is no official language, but the two most commonly taught and spoken are English and Hindi. Medical schools in India teach exclusively in English, and thus Indian doctors may require interpreters if their patients speak languages with which they are unfamiliar.
Kapasi works as an interpreter for a doctor due to his fluency in several languages. Ironically, though, his linguistic expertise is not matched by his cultural knowledge, and thus he fails to understand Mrs. Das, who is a westernized woman of Indian descent.