During the Renew Grace Period, most domain name extensions can be renewed from your client area at a regular price.
When reaching this period the domain will not resolve your DNS servers and therefore it will stop working. You can see the time during which the domain is found in this state by accessing to the information page of the domain extension(.com, .es, etc.).
If the domain is renewed during this period
If you renew the domain during this period, after a few hours it will work normally.
In the case that you don't renew during this period
If you have not renewed the domain and have spent the days that are in this state, the domain will to rule the next state depending on the domain extension, for example, in the case of a .com the state would be Redemption period.