If a domain is not renewed before its expiration date, it will be suspended by the registrar, breaking any email and web traffic destined to the domain.
There is a 40 day Grace Period during which the original registrant may renew their expired domain for the normal renewal price.
At this point the domain enters a 30 day Redemption Period. During this time the the domain may still be renewed by the original registrant, but the process is longer, more involved, and more costly. The normal price of the renewal plus a $109.80 USD Redemption Fee is required to restore the domain.
After this period, the domain will go into a 'Pending Delete' stage, the length of time of which varies per TLD, after which the domain will become available for anyone to register.