Block cipher does not provide security by itself What is this statement all about? When I look at a block cipher it seems pretty hard to break it and the mathematics behind insure a good complexity. It may refer to key generation, initialization vector (IV), padding scheme ?
That statement is ambiguous, so I'll list a couple of limitation of block ciphers and cryptography in general:


A raw blockcipher by itself only permutes a fixed size block (128 bits for AES). You need to add a mode of operation (together with IVs and possibly padding) to make it flexible enough for practical use. There are many modes to choose from, including CBC, CTR, OCB, SIV, GCM and XTS. Each one has different properties and strength, so which one is best depends on the the situation.
Encryption without integrity checks (e.g. using AES in CBC mode) is often vulnerable to active attacks, so you need to add a MAC. A modern trend is to use a mode-of-operation that provides both integrity and confidentiality (authenticated encryption, AEAD).
Encryption reduces a confidentiality problem to a key management problem. You still need to solve the key management problem.
Cryptography doesn't provide security by itself. You always need to consider the larger system. This includes endpoint security, threat models, key and identity management and much more.