Encryption only provides confidentiality. Authentication only can ensure integrity as it prevents illegal modification of data. Encryption + authentication offers both confidentiality and integrity.
Now the question comes why confidentiality alone is not enough or integrity alone is not enough. Encryption is usually done in various modes such as ECB, CBC, OFB, CFB etc. Each mode has some own advantages as well as limitations.
As a first step, consider ECB. This is the simplest mode.
As an attacker you can easily remove some encrypted blocks and the receiver will not know this. (Although it is not so simple but just as an example). Consider the following sentence and assume each word is a block which will be encrypted in ECB mode.
I am not coming today
. If the attacker removes
" block, the receiver will receive
I am coming today
Now consider CBC mode. In this case, cipher output of one block is used as an input in the next block. Now if you as an attacker want to remove one of those blocks although the next block will need the removed block but only few bits will be affected and the error will not propogate to the next block. This can be exploited by attackers to launch cut and paste attacks.
On the other hand, in case only authentication is applied, confidentiality cannot be ensured. Even if application layer encryption is applied, it means that only that original data packet is encrypted but not the additional header attached to that data in each successive layer. Data link layer encryption provides confidentiality for that additional information present in the headers.