I have heard it said that being redeemed is going from bondage to sin into new freedom of life. Christ bought us back from our bondage. There are other instances in the bible of the redeemer concept such as Ruth and the book of Isaiah. Here's an interesting tidbit from Wikipedia:
Goel (the Go’el HaDahm) is a Hebrew term which comes from the word lig'ol ("to redeem"), hence meaning "redeemer", which in the Hebrew Bible and the rabbinical tradition denotes a person who as the nearest relative of another is charged with the duty of restoring the rights of another and avenging his wrongs.