When your domain expires the DNS stops resolving or pointing your website and any email accounts associated with the domain name to the correct servers.
DNS stands for "Domain Name System". It helps users find their way around the Internet. Every computer on the Internet has a unique address, like a telephone number or address, consisting of a series of numbers known as an "IP address". DNS allows a familiar string of letters (eg. yourdomain.com) to be used instead of IP addresses, making the process of finding and remembering a web site's location easier. Translating a domain name into an IP address is referred to as "resolving" the domain name.
Once you have successfully renewed the domain name. The DNS will take time to propagate. DNS Propagation is the replicating of the DNS information around the entire internet, this needs to happen when a new domain name is registered or an existing one is transferred to a new DNS or the domain expires and is renewed. This process usually takes around 24 - 48 hours. During this time your website/email related to your domain name may not be accessible by some or all people. After the 24 - 48 hour propagation period your website/email should be working normally again.