As IPv4 addresses run out, more and more services are becoming available over IPv6. For a domain to open for users whose providers already hand out IPv6, it must have an AAAA record. When a browser resolves a name, it asks the DNS server for both types of records at once — A and AAAA — and picks an address depending on which protocol is available. Exactly how this happens is described in the article How a browser works.
In practice a domain usually has both records at the same time:
This way a single domain serves both old and new networks without changing the address for the user.