Well the obvious reason for a ringtone is to alert the phone owner that they have an incoming call that should be attended to.
It could be argued that ringtones are not important at all and just cause a public nuisance.

can ringtones give an indication of an owners personality?
It is certainly possible, as it gives an indication to people's personal tastes and quirkiness. Having a loud and annoying ringtone may indicate a need to be acknowledge.