Caucasian actually has two meanings. The term was coined by anthropologists in the 19th century to mean virtually any white person including people from India. These days it can mean somebody from the Caucasus or just a white person but it's now and outdated term.
I'm caucasian because I'm from the Caucasus region. So why do white people from Europe/America call themselves caucasian?
From the dictionary:
Caucasian---1. A white person; a person of European origin.
---2. A person from the Caucasus.
There are exceptions !
At one time is was believed (with very little evidence, I think) that the pale skinned "European" races originated in the Caucasus. Hence "Caucasian".
And, as somebody else already pointed out, it's less politically-loaded than "white"...