How exactly does AES-NI work? I am looking in to AES-NI which is now supported by many new CPU's and I have read a few papers which states that AES-CBC works faster with AES-NI, but I am unable to understand how exactly AES-NI works. 

As far as I know, AES-CBC encryption is sequential, so how does AES-NI make it so faster? 

(Also even after using AES-NI, is AES-CBC performed sequentially?)
AES-NI is just a fast way for the processor to execute the calculations of AES. Normally the computer has to calculate every single step of the AES key schedule and the rounds as a single instruction: Substitute it with the S-boxes, shift the rows, mix the columns, XOR the round key. This is called a software implementation. Every instruction has to be done in software from the program.

Using the AES instruction set the program can do a whole round in a single instruction. There are several different instructions to do this: New instructions, Wikipedia.
The instructions will be executed on hardware level, in the transistors of the processor. Without the whole other things a processor normally does to execute a program the encryption and decryption are much more efficient. This is called a hardware implementation. As far as I know, every block cipher is more efficient in hardware than in software. Some more, some not so much. "More efficient" means faster, less energy-consuming or both.

Yes, AES-CBC encryption still has to be done sequentially. AES-NI can only help with one encryption or decryption, but it still greatly increases the speed, because the encryption or decryption is the slowest part of CBC mode. (For the sake of completeness: You can use AES-NI for every encryption mode, not only CBC.)