A domain, if not renewed, expires on its expiration date. You can find this date in the so called whois record. Domain renewal with HelpingHost.com costs $12.95 per year.
40 days after the expiration, the domain can not be simply renewed it enters the state of redemption.
It ends 75 days past the expiration date. During the redemption period you are still able to renew the domain but it will cost $100 plus the normal $12.95 renewal fee. The reason is the amount of manual steps and cost that is involved for us to get the domain out of redemption.
After that, if not renewed, the domain will be released to be registered by anybody.