ticket_lifetime: Every ticket has a life time which is usually less than a day. After this period the ticket considered as expired and you are no longer be able to use your ticket. You have to obtain another one.
The renewable tickets have another property: renew_lifetime:
E.g. if your ticket has 7d renew_lifetime you can renew your ticket (with kinit -R) for 7d without typing you password again and the expiration date will be current date + ticket_lifetime. It is important that you cannot renew an expired ticket.
So you have 24h as ticket_lifetime and 7d as renew_lifetime. If you acquire your ticket on Monday 00:00 you can use your ticket until Tuesday 00:00. Before it expires (before Tuesday) you can renew it with kinit -R (and you have to renew it every day). With other words renew_lifetime is the maximum lifetime of a ticket.
As I mentioned earlier once a ticket expired (by its ticket_lifetime) you cannot renew it.