UD codes can only be interpreted in one way.
That is to say, that there is no ambiguity in turning a codeword back into its message.

Example One
 
Code with symbols A: 0 and B: 00.
Codeword: 000
 
000 could be translated to AB, BA or AAA.
Therefore our codes are NOT uniquely decodable.

Example Two
 
Code with symbols A: 0 and B: 1.
Codeword: 010
 
Uniquely decodable: ABA

Example Three  
Code with symbols A: 11, B: 01, C: 011
Codeword: 011101
 
Going left to right, we might be unsure if the first code is B or C.
However, the code is still uniquely decodable as we can decode it right to left.
Message: BAB