What is the role of IV in Stream Cipher? Why is it needed and what is it's importance? I ran into this problem when I read the stream ciphers and did not find a satisfactory answer. 

Why is an IV needed in stream ciphers, and what is the importance of using it?
Take a cipher, any cipher, and suppose the key is used for multiple messages.

Suppose that two messages happen to be identical. If the ciphertext depends only on the key and the message, then the ciphertexts for these messages will be identical. This leaks information about the messages. There are scenarios where this doesn't matter, but conversely, there are scenarios where it matters. Therefore any cipher uses a nonce in addition to the key. In ciphers that use an IV (or something related such as an initial counter value), the IV is this nonce

The nonce must have at least the property that the sender never performs two encryption operations with the same nonce. (Encrypting distinct messages with the same nonce would leak the fact that the messages are distinct.) Depending on the role that the IV plays in the cipher, there may be additional constraints.

With a stream cipher, the effects of encrypting twice with the same key and without using a nonce are rather devastating. Write $M[i]$ for the $i$th bit of the message and $C[i]$ for the $i$th bit of the ciphertext; then $C[i] = S[i] \oplus M[i]$ where $S$ is the keystream. If $S$ only depends on the key, then an adversary who obtains two ciphertexts $C_1$ and $C_2$ obtains $M_1 \oplus M_2 = S = C_1 \oplus C_2$. Guessing one bit of one message automatically reveals the bit in the same position in the other message.

The remedy is to ensure that the same keystream is never used twice. This can be done by ensuring that the key is only ever used once, or by incorporating a nonce (an IV) in the way the keystream is derived from the key.