Availability Groups are a new feature of SQL Server 2012 that provide continuous data synchronization, automatic failover and secondary read access for one or many SQL Server databases.
Availability Groups are different from Database Mirroring in several ways. The major differences are mostly centered around the ability to read the data on multiple other instances and the capabilities around automatic failover.
Official Info: An availability group supports a failover environment for a discrete set of user databases, known as availability databases, that fail over together. An availability group supports a set of primary databases and one to four sets of corresponding secondary databases. Source: http://msdn.microsoft.com/en-us/library/ff877884.aspx
Provides an integrated set of options including automatic and manual failover of a group of databases, support for up to four secondaries including two synchronous secondaries and seamless application failover using availability group listener. Source: http://www.microsoft.com/sqlserver/en/us/solutions-technologies/mission-critical-operations/SQL-Server-2012-high-availability.aspx
Resource: For more information on the capabilities and latest improvements to SQL Server Availability Groups you can visit the AlwaysOn Team Blog
Note that Availability Groups are part of and sometimes referred to as "AlwaysOn" - but "AlwaysOn" is a marketing term that refers to all of Microsoft's high availability and disaster recovery features over multiple server technologies.