how did hermione changed in bellatrix and why?

Hermione used Polyjuice Potion.
She did so to enter Gringotts and access Bellatrix' vault there, to retrieve Helga Hufflepuff's cup, one of Voldemort's horcruxes.
Check Chapter 26 "Gringotts" (I think I got it right).

Im assuming you mean how did Hermione change into Bellatrix.

She used a polyjuice potion, while getting tourtured some of Bellatrix's hair got on Hermione and she used that. The reason being Bellatrix in freaking out about the sopward of gryffendor implyed that something important was in her vault in gringotts. Harry assumed it was a horcrux so they disguised Hermione as Bellatrix to break into gringorrs and steal the horcrux.