With randomized encryption, ciphertexts must be slightly longer than plaintexts in order to allow for more than one possible ciphertext per plaintext Can anyone give me a simple example of this? 


  "For example, if there are $2^{64}$ possible cipher texts per plain text,
  cipher texts must be at least 64 bits longer than plain texts"


This is what book said but I don't really get this.
Think about it in the other direction; there are $2^{64}$ ciphertexts which will all decrypt to the same plaintext, and this holds for every plaintext.  There are a total of $2^n$ plaintexts of length $n$; hence, there must be $2^{64} \cdot 2^n = 2^{n+64}$ distinct ciphertexts which all decrypt to plaintexts of length $n$.  If we assume that all those ciphertexts are the same length, they must be at least $n+64$ bits long (because there aren't enough ciphertexts of shorter length).

Of course, if we don't require all the ciphertext lengths to be the same length, then it is possible that some of the ciphertexts may be shorter than $n+64$ bits (but only at the cost of having other ciphertexts be more than 64 bits longer than the corresponding plaintext).