There are many theories and reason why animê features large eyes, the most commonly accepted one is as follows.
Osamu Tezuka, known as "the father of manga", started drawing desenhos animados with large eyes in his earliest works because he got much of his inspiration from Walt disney and other Western animations (Bambi, Betty Boop, Snow White, all have large eyes). Due to the popularity of his works, the style has kept all these years.
Other reasons include: Large eyes have often been a characteristic of beauty
Large eyes make it easy to convey many different types of emotion
The Japanese phrase of "The eyes are the window to the soul"