^ (caret) means that all your returns should start with whatever directly follows the sign. Searching for first name ^Ann* will return everyone with a first name beginning with "ann". Which means Annelise will be returned, but Mari Anne will not.
$ (dollar sign) means that all your returns should end in what precedes the sign. Searching for surname *set$ will return all surnames ending in "set". "Furuset Nilsen" will not be included in your hitlist, while "Nilsen Furuset" will be.