I'm running Ubuntu 14.04 (LTS). When I go to System Details, under graphics, it shows 'VESA: BONAIRE', but I have a AMD Radeon R7 260X. Is this normal? Do I have to install extra drivers? Please let me know.
No you do not need extra drivers, these should be fine. Bonaire is a code name for a certain chip. AMD and Nvidia do a whole lot of re-branding of older models on a yearly basis (because OEMs force them to come up with updated model numbers that suggest significantly more performance), so don't be confused when you find this code name in earlier generations.
Radeon R7 260X
Radeon R7 260X was announced on September 25, 2013. With a launch price of $139, it is based on the Bonaire XTX chip, a faster iteration of Bonaire XT that the Radeon HD 7790 is based on.